\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\citation{DNT}
\@writefile{brf}{\backcite{DNT}{{8}{(document)}{Doc-Start}}}
\citation{Gag86}
\citation{HP89}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Maintenance Issues for the \textsf  {GAP} Character Table Library}}{10}{chapter.1}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:maintain}{{1}{10}{\textcolor {Chapter }{Maintenance Issues for the \textsf {GAP} Character Table Library}}{chapter.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{Disproving Possible Character Tables (November 2006)}}{10}{section.1.1}\protected@file@percent }
\newlabel{sect:disprove}{{1.1}{10}{\textcolor {Chapter }{Disproving Possible Character Tables (November 2006)}}{section.1.1}{}}
\@writefile{brf}{\backcite{Gag86}{{10}{1.1}{section.1.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{A Perfect Pseudo Character Table (November 2006)}}{10}{subsection.1.1.1}\protected@file@percent }
\newlabel{subsect:perfect_pseudo}{{1.1.1}{10}{\textcolor {Chapter }{A Perfect Pseudo Character Table (November 2006)}}{subsection.1.1.1}{}}
\@writefile{brf}{\backcite{HP89}{{10}{1.1.1}{subsection.1.1.1}}}
\citation{HP89}
\citation{HP89}
\citation{CP96}
\@writefile{brf}{\backcite{HP89}{{13}{1.1.1}{subsection.1.1.1}}}
\@writefile{brf}{\backcite{HP89}{{13}{1.1.1}{subsection.1.1.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.2}\textcolor {Chapter }{An Error in the Character Table of $E_6(2)$ (March 2016)}}{13}{subsection.1.1.2}\protected@file@percent }
\newlabel{subsect:errorE62}{{1.1.2}{13}{\textcolor {Chapter }{An Error in the Character Table of $E_6(2)$ (March 2016)}}{subsection.1.1.2}{}}
\@writefile{brf}{\backcite{CP96}{{13}{1.1.2}{subsection.1.1.2}}}
\citation{BMO17}
\citation{CP96}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.3}\textcolor {Chapter }{An Error in a Power Map of the Character Table of $2.F_4(2).2$ (November 2015)}}{14}{subsection.1.1.3}\protected@file@percent }
\newlabel{subsect:error2F422}{{1.1.3}{14}{\textcolor {Chapter }{An Error in a Power Map of the Character Table of $2.F_4(2).2$ (November 2015)}}{subsection.1.1.3}{}}
\@writefile{brf}{\backcite{BMO17}{{14}{1.1.3}{subsection.1.1.3}}}
\@writefile{brf}{\backcite{CP96}{{14}{1.1.3}{subsection.1.1.3}}}
\citation{Ost86}
\citation{NPP84}
\citation{Bre91}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.4}\textcolor {Chapter }{A Character Table with a Wrong Name (May 2017)}}{15}{subsection.1.1.4}\protected@file@percent }
\newlabel{subsect:LyN2}{{1.1.4}{15}{\textcolor {Chapter }{A Character Table with a Wrong Name (May 2017)}}{subsection.1.1.4}{}}
\@writefile{brf}{\backcite{Ost86}{{15}{1.1.4}{subsection.1.1.4}}}
\@writefile{brf}{\backcite{NPP84}{{15}{1.1.4}{subsection.1.1.4}}}
\@writefile{brf}{\backcite{Bre91}{{15}{1.1.4}{subsection.1.1.4}}}
\citation{HP89}
\citation{HP89}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{Some finite factor groups of perfect space groups (February 2014)}}{16}{section.1.2}\protected@file@percent }
\newlabel{sect:spacegroupfactors}{{1.2}{16}{\textcolor {Chapter }{Some finite factor groups of perfect space groups (February 2014)}}{section.1.2}{}}
\@writefile{brf}{\backcite{HP89}{{16}{1.2}{section.1.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{Constructing the space groups in question}}{16}{subsection.1.2.1}\protected@file@percent }
\newlabel{subsect:constructspacegroups}{{1.2.1}{16}{\textcolor {Chapter }{Constructing the space groups in question}}{subsection.1.2.1}{}}
\@writefile{brf}{\backcite{HP89}{{16}{1.2.1}{subsection.1.2.1}}}
\citation{HP89}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}\textcolor {Chapter }{Constructing the factor groups in question}}{17}{subsection.1.2.2}\protected@file@percent }
\newlabel{subsect:constructfactors}{{1.2.2}{17}{\textcolor {Chapter }{Constructing the factor groups in question}}{subsection.1.2.2}{}}
\@writefile{brf}{\backcite{HP89}{{17}{1.2.2}{subsection.1.2.2}}}
\@writefile{brf}{\backcite{HP89}{{17}{1.2.2}{subsection.1.2.2}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.3}\textcolor {Chapter }{Examples with point group $A_5$}}{18}{subsection.1.2.3}\protected@file@percent }
\newlabel{subsect:expl-A5}{{1.2.3}{18}{\textcolor {Chapter }{Examples with point group $A_5$}}{subsection.1.2.3}{}}
\@writefile{brf}{\backcite{HP89}{{18}{1.2.3}{subsection.1.2.3}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.4}\textcolor {Chapter }{Examples with point group $L_3(2)$}}{19}{subsection.1.2.4}\protected@file@percent }
\newlabel{subsect:expl-L32}{{1.2.4}{19}{\textcolor {Chapter }{Examples with point group $L_3(2)$}}{subsection.1.2.4}{}}
\@writefile{brf}{\backcite{HP89}{{19}{1.2.4}{subsection.1.2.4}}}
\citation{HP89}
\citation{HP89}
\citation{HP89}
\@writefile{brf}{\backcite{HP89}{{21}{1.2.4}{subsection.1.2.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.5}\textcolor {Chapter }{Example with point group SL$_2(7)$}}{21}{subsection.1.2.5}\protected@file@percent }
\newlabel{subsect:expl-sl27}{{1.2.5}{21}{\textcolor {Chapter }{Example with point group SL$_2(7)$}}{subsection.1.2.5}{}}
\@writefile{brf}{\backcite{HP89}{{21}{1.2.5}{subsection.1.2.5}}}
\citation{HP89}
\citation{HP89}
\@writefile{brf}{\backcite{HP89}{{22}{1.2.5}{subsection.1.2.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.6}\textcolor {Chapter }{Example with point group $2^3.L_3(2)$}}{22}{subsection.1.2.6}\protected@file@percent }
\newlabel{subsect:expl-23L32}{{1.2.6}{22}{\textcolor {Chapter }{Example with point group $2^3.L_3(2)$}}{subsection.1.2.6}{}}
\@writefile{brf}{\backcite{HP89}{{22}{1.2.6}{subsection.1.2.6}}}
\@writefile{brf}{\backcite{HP89}{{22}{1.2.6}{subsection.1.2.6}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.7}\textcolor {Chapter }{Examples with point group $A_6$}}{23}{subsection.1.2.7}\protected@file@percent }
\newlabel{subsect:expl-A6}{{1.2.7}{23}{\textcolor {Chapter }{Examples with point group $A_6$}}{subsection.1.2.7}{}}
\@writefile{brf}{\backcite{HP89}{{23}{1.2.7}{subsection.1.2.7}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.8}\textcolor {Chapter }{Examples with point group $L_2(8)$}}{25}{subsection.1.2.8}\protected@file@percent }
\newlabel{subsect:expl-L28}{{1.2.8}{25}{\textcolor {Chapter }{Examples with point group $L_2(8)$}}{subsection.1.2.8}{}}
\@writefile{brf}{\backcite{HP89}{{25}{1.2.8}{subsection.1.2.8}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.9}\textcolor {Chapter }{Example with point group $M_{11}$}}{26}{subsection.1.2.9}\protected@file@percent }
\newlabel{subsect:expl-M11}{{1.2.9}{26}{\textcolor {Chapter }{Example with point group $M_{11}$}}{subsection.1.2.9}{}}
\@writefile{brf}{\backcite{HP89}{{26}{1.2.9}{subsection.1.2.9}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.10}\textcolor {Chapter }{Example with point group $U_3(3)$}}{27}{subsection.1.2.10}\protected@file@percent }
\newlabel{subsect:expl-U33}{{1.2.10}{27}{\textcolor {Chapter }{Example with point group $U_3(3)$}}{subsection.1.2.10}{}}
\@writefile{brf}{\backcite{HP89}{{27}{1.2.10}{subsection.1.2.10}}}
\citation{HP89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.11}\textcolor {Chapter }{Examples with point group $U_4(2)$}}{28}{subsection.1.2.11}\protected@file@percent }
\newlabel{subsect:expl-U42}{{1.2.11}{28}{\textcolor {Chapter }{Examples with point group $U_4(2)$}}{subsection.1.2.11}{}}
\@writefile{brf}{\backcite{HP89}{{28}{1.2.11}{subsection.1.2.11}}}
\citation{NR14}
\citation{JLPW95}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.12}\textcolor {Chapter }{A remark on one of the example groups}}{29}{subsection.1.2.12}\protected@file@percent }
\newlabel{subsect:A-remark-on-one-of-the-example-groups}{{1.2.12}{29}{\textcolor {Chapter }{A remark on one of the example groups}}{subsection.1.2.12}{}}
\@writefile{brf}{\backcite{NR14}{{29}{1.2.12}{subsection.1.2.12}}}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{Generality problems (December 2004/October 2015)}}{29}{section.1.3}\protected@file@percent }
\newlabel{sect:generalityproblems}{{1.3}{29}{\textcolor {Chapter }{Generality problems (December 2004/October 2015)}}{section.1.3}{}}
\@writefile{brf}{\backcite{JLPW95}{{29}{1.3}{section.1.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}\textcolor {Chapter }{Listing possible generality problems}}{29}{subsection.1.3.1}\protected@file@percent }
\newlabel{subsect:generalityproblems_list}{{1.3.1}{29}{\textcolor {Chapter }{Listing possible generality problems}}{subsection.1.3.1}{}}
\citation{JLPW95}
\@writefile{brf}{\backcite{JLPW95}{{34}{1.3.1}{subsection.1.3.1}}}
\citation{JLPW95}
\citation{AGRv3}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}\textcolor {Chapter }{A generality problem concerning the group $J_3$ (April 2015)}}{38}{subsection.1.3.2}\protected@file@percent }
\newlabel{subsect:generality_J3}{{1.3.2}{38}{\textcolor {Chapter }{A generality problem concerning the group $J_3$ (April 2015)}}{subsection.1.3.2}{}}
\@writefile{brf}{\backcite{JLPW95}{{38}{1.3.2}{subsection.1.3.2}}}
\@writefile{brf}{\backcite{AGRv3}{{38}{1.3.2}{subsection.1.3.2}}}
\citation{JLPW95}
\citation{JLPW95}
\@writefile{brf}{\backcite{JLPW95}{{39}{1.3.2}{subsection.1.3.2}}}
\newlabel{valuesJ3}{{1.3.2}{39}{\textcolor {Chapter }{A generality problem concerning the group $J_3$ (April 2015)}}{subsection.1.3.2}{}}
\citation{HL89}
\citation{JLPW95}
\@writefile{brf}{\backcite{JLPW95}{{40}{1.3.2}{subsection.1.3.2}}}
\@writefile{brf}{\backcite{HL89}{{40}{1.3.2}{subsection.1.3.2}}}
\@writefile{brf}{\backcite{JLPW95}{{40}{1.3.2}{subsection.1.3.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}\textcolor {Chapter }{Brauer Tables that can be derived from Known Tables}}{40}{section.1.4}\protected@file@percent }
\newlabel{sect:derivebrauercharacters}{{1.4}{40}{\textcolor {Chapter }{Brauer Tables that can be derived from Known Tables}}{section.1.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}\textcolor {Chapter }{Brauer Tables via Construction Information}}{40}{subsection.1.4.1}\protected@file@percent }
\newlabel{sect:brauercharactersbyconstruction}{{1.4.1}{40}{\textcolor {Chapter }{Brauer Tables via Construction Information}}{subsection.1.4.1}{}}
\citation{HL89}
\citation{Dad66}
\citation{HL89}
\citation{HL89}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}\textcolor {Chapter }{Liftable Brauer Characters (May 2017)}}{41}{subsection.1.4.2}\protected@file@percent }
\newlabel{sect:liftablebrauercharacters}{{1.4.2}{41}{\textcolor {Chapter }{Liftable Brauer Characters (May 2017)}}{subsection.1.4.2}{}}
\@writefile{brf}{\backcite{HL89}{{41}{1.4.2}{subsection.1.4.2}}}
\@writefile{brf}{\backcite{Dad66}{{41}{1.4.2}{subsection.1.4.2}}}
\@writefile{brf}{\backcite{HL89}{{41}{1.4.2}{subsection.1.4.2}}}
\@writefile{brf}{\backcite{HL89}{{41}{1.4.2}{subsection.1.4.2}}}
\citation{GAP}
\citation{CTblLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Using Table Automorphisms for Constructing Character Tables in \textsf  {GAP}}}{43}{chapter.2}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:ctblcons}{{2}{43}{\textcolor {Chapter }{Using Table Automorphisms for Constructing Character Tables in \textsf {GAP}}}{chapter.2}{}}
\@writefile{brf}{\backcite{GAP}{{43}{2}{chapter.2}}}
\@writefile{brf}{\backcite{CTblLib}{{43}{2}{chapter.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{Overview}}{43}{section.2.1}\protected@file@percent }
\newlabel{sect:overview_ctblcons}{{2.1}{43}{\textcolor {Chapter }{Overview}}{section.2.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{Theoretical Background}}{43}{section.2.2}\protected@file@percent }
\newlabel{sect:theory}{{2.2}{43}{\textcolor {Chapter }{Theoretical Background}}{section.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{Character Table Automorphisms}}{43}{subsection.2.2.1}\protected@file@percent }
\newlabel{subsect:Character Table Automorphisms}{{2.2.1}{43}{\textcolor {Chapter }{Character Table Automorphisms}}{subsection.2.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}\textcolor {Chapter }{Permutation Equivalence of Character Tables}}{44}{subsection.2.2.2}\protected@file@percent }
\newlabel{sect:Permutation Equivalence of Character Tables}{{2.2.2}{44}{\textcolor {Chapter }{Permutation Equivalence of Character Tables}}{subsection.2.2.2}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}\textcolor {Chapter }{Class Fusions}}{45}{subsection.2.2.3}\protected@file@percent }
\newlabel{subsect:class_fusions}{{2.2.3}{45}{\textcolor {Chapter }{Class Fusions}}{subsection.2.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}\textcolor {Chapter }{Constructing Character Tables of Certain Isoclinic Groups}}{45}{subsection.2.2.4}\protected@file@percent }
\newlabel{subsect:isoclinism}{{2.2.4}{45}{\textcolor {Chapter }{Constructing Character Tables of Certain Isoclinic Groups}}{subsection.2.2.4}{}}
\@writefile{brf}{\backcite{CCN85}{{45}{2.2.4}{subsection.2.2.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.5}\textcolor {Chapter }{Character Tables of Isoclinic Groups of the Structure $p.G.p$ (October 2016)}}{46}{subsection.2.2.5}\protected@file@percent }
\newlabel{subsect:isoclinicP}{{2.2.5}{46}{\textcolor {Chapter }{Character Tables of Isoclinic Groups of the Structure $p.G.p$ (October 2016)}}{subsection.2.2.5}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.6}\textcolor {Chapter }{Isoclinic Double Covers of Almost Simple Groups}}{47}{subsection.2.2.6}\protected@file@percent }
\newlabel{subsect:isoclinicATLAS}{{2.2.6}{47}{\textcolor {Chapter }{Isoclinic Double Covers of Almost Simple Groups}}{subsection.2.2.6}{}}
\@writefile{brf}{\backcite{CCN85}{{47}{2.2.6}{subsection.2.2.6}}}
\citation{Feit82}
\citation{Feit82}
\citation{Nav98}
\citation{LP10}
\citation{Feit82}
\citation{Nav98}
\citation{LP10}
\citation{Feit82}
\citation{Nav98}
\citation{LP10}
\citation{Isa76}
\citation{Bre11}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.7}\textcolor {Chapter }{Characters of Normal Subgroups}}{49}{subsection.2.2.7}\protected@file@percent }
\newlabel{subsect:theorClifford}{{2.2.7}{49}{\textcolor {Chapter }{Characters of Normal Subgroups}}{subsection.2.2.7}{}}
\@writefile{brf}{\backcite{Feit82}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Feit82}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Nav98}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{LP10}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Feit82}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Nav98}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{LP10}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Feit82}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Nav98}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{LP10}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{brf}{\backcite{Isa76}{{49}{2.2.7}{subsection.2.2.7}}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{The Constructions}}{49}{section.2.3}\protected@file@percent }
\newlabel{sect:constr}{{2.3}{49}{\textcolor {Chapter }{The Constructions}}{section.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{Character Tables of Groups of the Structure $M.G.A$}}{49}{subsection.2.3.1}\protected@file@percent }
\newlabel{subsect:theorMGA}{{2.3.1}{49}{\textcolor {Chapter }{Character Tables of Groups of the Structure $M.G.A$}}{subsection.2.3.1}{}}
\@writefile{brf}{\backcite{Bre11}{{49}{2.3.1}{subsection.2.3.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{Character Tables of Groups of the Structure $G.S_3$}}{50}{subsection.2.3.2}\protected@file@percent }
\newlabel{sect:Character Tables of Groups of the Structure G.S_3}{{2.3.2}{50}{\textcolor {Chapter }{Character Tables of Groups of the Structure $G.S_3$}}{subsection.2.3.2}{}}
\citation{HL94}
\@writefile{brf}{\backcite{HL94}{{51}{2.3.2}{subsection.2.3.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}\textcolor {Chapter }{Character Tables of Groups of the Structure $G.2^2$}}{52}{subsection.2.3.3}\protected@file@percent }
\newlabel{subsect:theorGV4}{{2.3.3}{52}{\textcolor {Chapter }{Character Tables of Groups of the Structure $G.2^2$}}{subsection.2.3.3}{}}
\citation{Isa76}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.4}\textcolor {Chapter }{Character Tables of Groups of the Structure $2^2.G$ (August 2005)}}{53}{subsection.2.3.4}\protected@file@percent }
\newlabel{subsect:theorV4G}{{2.3.4}{53}{\textcolor {Chapter }{Character Tables of Groups of the Structure $2^2.G$ (August 2005)}}{subsection.2.3.4}{}}
\@writefile{brf}{\backcite{Isa76}{{53}{2.3.4}{subsection.2.3.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.5}\textcolor {Chapter }{$p$-Modular Tables of Extensions by $p$-singular Automorphisms}}{55}{subsection.2.3.5}\protected@file@percent }
\newlabel{subsect:theorpsing}{{2.3.5}{55}{\textcolor {Chapter }{$p$-Modular Tables of Extensions by $p$-singular Automorphisms}}{subsection.2.3.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.6}\textcolor {Chapter }{Character Tables of Subdirect Products of Index Two (July 2007)}}{56}{subsection.2.3.6}\protected@file@percent }
\newlabel{subsect:theorsubdir}{{2.3.6}{56}{\textcolor {Chapter }{Character Tables of Subdirect Products of Index Two (July 2007)}}{subsection.2.3.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{Examples for the Type $M.G.A$}}{57}{section.2.4}\protected@file@percent }
\newlabel{sect:explMGA}{{2.4}{57}{\textcolor {Chapter }{Examples for the Type $M.G.A$}}{section.2.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}\textcolor {Chapter }{Character Tables of Dihedral Groups}}{57}{subsection.2.4.1}\protected@file@percent }
\newlabel{subsect:dihedralMGA}{{2.4.1}{57}{\textcolor {Chapter }{Character Tables of Dihedral Groups}}{subsection.2.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}\textcolor {Chapter }{An $M.G.A$ Type Example with $M$ noncentral in $M.G$ (May 2004)}}{59}{subsection.2.4.2}\protected@file@percent }
\newlabel{subsect:A12N7}{{2.4.2}{59}{\textcolor {Chapter }{An $M.G.A$ Type Example with $M$ noncentral in $M.G$ (May 2004)}}{subsection.2.4.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}\textcolor {Chapter }{\textsf  {Atlas} Tables of the Type $M.G.A$}}{60}{subsection.2.4.3}\protected@file@percent }
\newlabel{subsect:ATLASMGA}{{2.4.3}{60}{\textcolor {Chapter }{\textsf {Atlas} Tables of the Type $M.G.A$}}{subsection.2.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.4}\textcolor {Chapter }{More \textsf  {Atlas} Tables of the Type $M.G.A$}}{65}{subsection.2.4.4}\protected@file@percent }
\newlabel{subsect:MoreATLASMGA}{{2.4.4}{65}{\textcolor {Chapter }{More \textsf {Atlas} Tables of the Type $M.G.A$}}{subsection.2.4.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.5}\textcolor {Chapter }{The Character Tables of $4_2.L_3(4).2_3$ and $12_2.L_3(4).2_3$}}{68}{subsection.2.4.5}\protected@file@percent }
\newlabel{subsect:4_2.L_3(4).2_3}{{2.4.5}{68}{\textcolor {Chapter }{The Character Tables of $4_2.L_3(4).2_3$ and $12_2.L_3(4).2_3$}}{subsection.2.4.5}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{69}{2.4.5}{subsection.2.4.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.6}\textcolor {Chapter }{The Character Tables of $12_1.U_4(3).2_2'$ and $12_2.U_4(3).2_3'$ (December{\nobreakspace  }2015)}}{70}{subsection.2.4.6}\protected@file@percent }
\newlabel{subsect:12_i.U_4(3).2_jdash}{{2.4.6}{70}{\textcolor {Chapter }{The Character Tables of $12_1.U_4(3).2_2'$ and $12_2.U_4(3).2_3'$ (December{\nobreakspace }2015)}}{subsection.2.4.6}{}}
\citation{BN95}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.7}\textcolor {Chapter }{Groups of the Structures $3.U_3(8).3_1$ and $3.U_3(8).6$ (February 2017)}}{71}{subsection.2.4.7}\protected@file@percent }
\newlabel{subsect:struct3U3831}{{2.4.7}{71}{\textcolor {Chapter }{Groups of the Structures $3.U_3(8).3_1$ and $3.U_3(8).6$ (February 2017)}}{subsection.2.4.7}{}}
\@writefile{brf}{\backcite{BN95}{{71}{2.4.7}{subsection.2.4.7}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.8}\textcolor {Chapter }{The Character Table of $(2^2 \times F_4(2)):2 < B$ (March{\nobreakspace  }2003)}}{73}{subsection.2.4.8}\protected@file@percent }
\newlabel{subsect:BM6}{{2.4.8}{73}{\textcolor {Chapter }{The Character Table of $(2^2 \times F_4(2)):2 < B$ (March{\nobreakspace }2003)}}{subsection.2.4.8}{}}
\@writefile{brf}{\backcite{CCN85}{{73}{2.4.8}{subsection.2.4.8}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.9}\textcolor {Chapter }{The Character Table of $2.(S_3 \times Fi_{22}.2) < 2.B$ (March{\nobreakspace  }2003)}}{75}{subsection.2.4.9}\protected@file@percent }
\newlabel{subsect:2.BM9}{{2.4.9}{75}{\textcolor {Chapter }{The Character Table of $2.(S_3 \times Fi_{22}.2) < 2.B$ (March{\nobreakspace }2003)}}{subsection.2.4.9}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.10}\textcolor {Chapter }{The Character Table of $(2 \times 2.Fi_{22}):2 < Fi_{24}$ (November{\nobreakspace  }2008)}}{78}{subsection.2.4.10}\protected@file@percent }
\newlabel{subsect:(2x2.Fi22):2_in_Fi24}{{2.4.10}{78}{\textcolor {Chapter }{The Character Table of $(2 \times 2.Fi_{22}):2 < Fi_{24}$ (November{\nobreakspace }2008)}}{subsection.2.4.10}{}}
\@writefile{brf}{\backcite{CCN85}{{78}{2.4.10}{subsection.2.4.10}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.11}\textcolor {Chapter }{The Character Table of $S_3 \times 2.U_4(3).2_2 \leq 2.Fi_{22}$ (September 2002)}}{79}{subsection.2.4.11}\protected@file@percent }
\newlabel{subsect:S_3x2.U_4(3).2_2_in_2.Fi22}{{2.4.11}{79}{\textcolor {Chapter }{The Character Table of $S_3 \times 2.U_4(3).2_2 \leq 2.Fi_{22}$ (September 2002)}}{subsection.2.4.11}{}}
\@writefile{brf}{\backcite{CCN85}{{79}{2.4.11}{subsection.2.4.11}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.12}\textcolor {Chapter }{The Character Table of $4.HS.2 \leq HN.2$ (May 2002)}}{80}{subsection.2.4.12}\protected@file@percent }
\newlabel{subsect:HN2}{{2.4.12}{80}{\textcolor {Chapter }{The Character Table of $4.HS.2 \leq HN.2$ (May 2002)}}{subsection.2.4.12}{}}
\@writefile{brf}{\backcite{CCN85}{{80}{2.4.12}{subsection.2.4.12}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.13}\textcolor {Chapter }{The Character Tables of $4.A_6.2_3$, $12.A_6.2_3$, and $4.L_2(25).2_3$}}{83}{subsection.2.4.13}\protected@file@percent }
\newlabel{subsect:4.A_6.2_3, 12.A_6.2_3, 4.L_2(25).2_3}{{2.4.13}{83}{\textcolor {Chapter }{The Character Tables of $4.A_6.2_3$, $12.A_6.2_3$, and $4.L_2(25).2_3$}}{subsection.2.4.13}{}}
\@writefile{brf}{\backcite{CCN85}{{83}{2.4.13}{subsection.2.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{83}{2.4.13}{subsection.2.4.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{84}{2.4.13}{subsection.2.4.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{85}{2.4.13}{subsection.2.4.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{86}{2.4.13}{subsection.2.4.13}}}
\citation{CCN85}
\citation{JLPW95}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.14}\textcolor {Chapter }{The Character Table of $4.L_2(49).2_3$ (December 2020)}}{89}{subsection.2.4.14}\protected@file@percent }
\newlabel{subsect:4.L_2(49).2_3}{{2.4.14}{89}{\textcolor {Chapter }{The Character Table of $4.L_2(49).2_3$ (December 2020)}}{subsection.2.4.14}{}}
\@writefile{brf}{\backcite{CCN85}{{89}{2.4.14}{subsection.2.4.14}}}
\@writefile{brf}{\backcite{JLPW95}{{89}{2.4.14}{subsection.2.4.14}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.15}\textcolor {Chapter }{The Character Table of $4.L_2(81).2_3$ (December 2020)}}{91}{subsection.2.4.15}\protected@file@percent }
\newlabel{subsect:4.L_2(81).2_3}{{2.4.15}{91}{\textcolor {Chapter }{The Character Table of $4.L_2(81).2_3$ (December 2020)}}{subsection.2.4.15}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.16}\textcolor {Chapter }{The Character Table of $9.U_3(8).3_3$ (March 2017)}}{92}{subsection.2.4.16}\protected@file@percent }
\newlabel{subsect:9.U_3(8).3_3}{{2.4.16}{92}{\textcolor {Chapter }{The Character Table of $9.U_3(8).3_3$ (March 2017)}}{subsection.2.4.16}{}}
\@writefile{brf}{\backcite{CCN85}{{92}{2.4.16}{subsection.2.4.16}}}
\citation{Gag86}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.17}\textcolor {Chapter }{Pseudo Character Tables of the Type $M.G.A$ (May 2004)}}{97}{subsection.2.4.17}\protected@file@percent }
\newlabel{subsect:pseudo}{{2.4.17}{97}{\textcolor {Chapter }{Pseudo Character Tables of the Type $M.G.A$ (May 2004)}}{subsection.2.4.17}{}}
\@writefile{brf}{\backcite{Gag86}{{97}{2.4.17}{subsection.2.4.17}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{99}{2.4.17}{subsection.2.4.17}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.18}\textcolor {Chapter }{Some Extra-ordinary $p$-Modular Tables of the Type $M.G.A$ (September 2005)}}{100}{subsection.2.4.18}\protected@file@percent }
\newlabel{subsect:Extra-ordinary p-Modular Tables of the Type M.G.A}{{2.4.18}{100}{\textcolor {Chapter }{Some Extra-ordinary $p$-Modular Tables of the Type $M.G.A$ (September 2005)}}{subsection.2.4.18}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.5}\textcolor {Chapter }{Examples for the Type $G.S_3$}}{103}{section.2.5}\protected@file@percent }
\newlabel{sect:GS3}{{2.5}{103}{\textcolor {Chapter }{Examples for the Type $G.S_3$}}{section.2.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.1}\textcolor {Chapter }{Small Examples}}{103}{subsection.2.5.1}\protected@file@percent }
\newlabel{sect:Small Examples}{{2.5.1}{103}{\textcolor {Chapter }{Small Examples}}{subsection.2.5.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.2}\textcolor {Chapter }{\textsf  {Atlas} Tables of the Type $G.S_3$}}{104}{subsection.2.5.2}\protected@file@percent }
\newlabel{subsect:xplGS3}{{2.5.2}{104}{\textcolor {Chapter }{\textsf {Atlas} Tables of the Type $G.S_3$}}{subsection.2.5.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.6}\textcolor {Chapter }{Examples for the Type $G.2^2$}}{108}{section.2.6}\protected@file@percent }
\newlabel{sect:xplGV4}{{2.6}{108}{\textcolor {Chapter }{Examples for the Type $G.2^2$}}{section.2.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.1}\textcolor {Chapter }{The Character Table of $A_6.2^2$}}{108}{subsection.2.6.1}\protected@file@percent }
\newlabel{sect:The Character Table of A_6.2^2}{{2.6.1}{108}{\textcolor {Chapter }{The Character Table of $A_6.2^2$}}{subsection.2.6.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.2}\textcolor {Chapter }{\textsf  {Atlas} Tables of the Type $G.2^2$ {\textendash } Easy Cases}}{109}{subsection.2.6.2}\protected@file@percent }
\newlabel{subsect:xplGV43.A6.V4}{{2.6.2}{109}{\textcolor {Chapter }{\textsf {Atlas} Tables of the Type $G.2^2$ {\textendash } Easy Cases}}{subsection.2.6.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.3}\textcolor {Chapter }{The Character Table of $S_4(9).2^2$ (September 2011)}}{114}{subsection.2.6.3}\protected@file@percent }
\newlabel{subsect:The Character Table of S_4(9).2^2}{{2.6.3}{114}{\textcolor {Chapter }{The Character Table of $S_4(9).2^2$ (September 2011)}}{subsection.2.6.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.4}\textcolor {Chapter }{The Character Tables of Groups of the Type $2.L_3(4).2^2$ (June 2010)}}{115}{subsection.2.6.4}\protected@file@percent }
\newlabel{subsect:2L34V4}{{2.6.4}{115}{\textcolor {Chapter }{The Character Tables of Groups of the Type $2.L_3(4).2^2$ (June 2010)}}{subsection.2.6.4}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{117}{2.6.4}{subsection.2.6.4}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{118}{2.6.4}{subsection.2.6.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.5}\textcolor {Chapter }{The Character Tables of Groups of the Type $6.L_3(4).2^2$ (October 2011)}}{119}{subsection.2.6.5}\protected@file@percent }
\newlabel{subsect:6L34V4}{{2.6.5}{119}{\textcolor {Chapter }{The Character Tables of Groups of the Type $6.L_3(4).2^2$ (October 2011)}}{subsection.2.6.5}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{122}{2.6.5}{subsection.2.6.5}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.6}\textcolor {Chapter }{The Character Tables of Groups of the Type $2.U_4(3).2^2$ (February 2012)}}{123}{subsection.2.6.6}\protected@file@percent }
\newlabel{subsect:2U43V4}{{2.6.6}{123}{\textcolor {Chapter }{The Character Tables of Groups of the Type $2.U_4(3).2^2$ (February 2012)}}{subsection.2.6.6}{}}
\@writefile{brf}{\backcite{CCN85}{{123}{2.6.6}{subsection.2.6.6}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{124}{2.6.6}{subsection.2.6.6}}}
\@writefile{brf}{\backcite{CCN85}{{124}{2.6.6}{subsection.2.6.6}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.7}\textcolor {Chapter }{The Character Tables of Groups of the Type $4_1.L_3(4).2^2$ (October 2011)}}{126}{subsection.2.6.7}\protected@file@percent }
\newlabel{subsect:41L34V4}{{2.6.7}{126}{\textcolor {Chapter }{The Character Tables of Groups of the Type $4_1.L_3(4).2^2$ (October 2011)}}{subsection.2.6.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.8}\textcolor {Chapter }{The Character Tables of Groups of the Type $4_2.L_3(4).2^2$ (October 2011)}}{130}{subsection.2.6.8}\protected@file@percent }
\newlabel{subsect:42L34V4}{{2.6.8}{130}{\textcolor {Chapter }{The Character Tables of Groups of the Type $4_2.L_3(4).2^2$ (October 2011)}}{subsection.2.6.8}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{134}{2.6.8}{subsection.2.6.8}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.9}\textcolor {Chapter }{The Character Table of Aut$(L_2(81))$}}{134}{subsection.2.6.9}\protected@file@percent }
\newlabel{subsect:Aut(L_2(81))}{{2.6.9}{134}{\textcolor {Chapter }{The Character Table of Aut$(L_2(81))$}}{subsection.2.6.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.10}\textcolor {Chapter }{The Character Table of $O_8^+(3).2^2_{111}$}}{135}{subsection.2.6.10}\protected@file@percent }
\newlabel{subsect:O_8^+(3).2^2_111}{{2.6.10}{135}{\textcolor {Chapter }{The Character Table of $O_8^+(3).2^2_{111}$}}{subsection.2.6.10}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2.7}\textcolor {Chapter }{Examples for the Type $2^2.G$}}{136}{section.2.7}\protected@file@percent }
\newlabel{sect:xplV4G}{{2.7}{136}{\textcolor {Chapter }{Examples for the Type $2^2.G$}}{section.2.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.7.1}\textcolor {Chapter }{The Character Table of $2^2.Sz(8)$}}{137}{subsection.2.7.1}\protected@file@percent }
\newlabel{subsect:2^2.Sz(8)}{{2.7.1}{137}{\textcolor {Chapter }{The Character Table of $2^2.Sz(8)$}}{subsection.2.7.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.7.2}\textcolor {Chapter }{\textsf  {Atlas} Tables of the Type $2^2.G$ (September 2005)}}{139}{subsection.2.7.2}\protected@file@percent }
\newlabel{subsect:V4GATLAS}{{2.7.2}{139}{\textcolor {Chapter }{\textsf {Atlas} Tables of the Type $2^2.G$ (September 2005)}}{subsection.2.7.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.7.3}\textcolor {Chapter }{The Character Table of $2^2.O_8^+(3)$ (March 2009)}}{143}{subsection.2.7.3}\protected@file@percent }
\newlabel{subsect:MultO8p3}{{2.7.3}{143}{\textcolor {Chapter }{The Character Table of $2^2.O_8^+(3)$ (March 2009)}}{subsection.2.7.3}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.7.4}\textcolor {Chapter }{The Character Table of the Schur Cover of $L_3(4)$ (September 2005)}}{144}{subsection.2.7.4}\protected@file@percent }
\newlabel{subsect:MultL34}{{2.7.4}{144}{\textcolor {Chapter }{The Character Table of the Schur Cover of $L_3(4)$ (September 2005)}}{subsection.2.7.4}{}}
\@writefile{brf}{\backcite{CCN85}{{144}{2.7.4}{subsection.2.7.4}}}
\@writefile{toc}{\contentsline {section}{\numberline {2.8}\textcolor {Chapter }{Examples of Extensions by $p$-singular Automorphisms}}{146}{section.2.8}\protected@file@percent }
\newlabel{sect:xplpsing}{{2.8}{146}{\textcolor {Chapter }{Examples of Extensions by $p$-singular Automorphisms}}{section.2.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.1}\textcolor {Chapter }{Some $p$-Modular Tables of Groups of the Type $M.G.A$}}{146}{subsection.2.8.1}\protected@file@percent }
\newlabel{subsect:Some p-Modular Tables of Groups of the Type M.G.A}{{2.8.1}{146}{\textcolor {Chapter }{Some $p$-Modular Tables of Groups of the Type $M.G.A$}}{subsection.2.8.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.2}\textcolor {Chapter }{Some $p$-Modular Tables of Groups of the Type $G.S_3$}}{147}{subsection.2.8.2}\protected@file@percent }
\newlabel{subsect:Some p-Modular Tables of Groups of the Type G.S_3}{{2.8.2}{147}{\textcolor {Chapter }{Some $p$-Modular Tables of Groups of the Type $G.S_3$}}{subsection.2.8.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.3}\textcolor {Chapter }{$2$-Modular Tables of Groups of the Type $G.2^2$}}{148}{subsection.2.8.3}\protected@file@percent }
\newlabel{subsect:2-Modular Tables of Groups of the Type G.2^2}{{2.8.3}{148}{\textcolor {Chapter }{$2$-Modular Tables of Groups of the Type $G.2^2$}}{subsection.2.8.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.8.4}\textcolor {Chapter }{The $3$-Modular Table of $U_3(8).3^2$}}{149}{subsection.2.8.4}\protected@file@percent }
\newlabel{subsect:The 3-Modular Table of U38.32}{{2.8.4}{149}{\textcolor {Chapter }{The $3$-Modular Table of $U_3(8).3^2$}}{subsection.2.8.4}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {2.9}\textcolor {Chapter }{Examples of Subdirect Products of Index Two}}{150}{section.2.9}\protected@file@percent }
\newlabel{sect:Gsubdir}{{2.9}{150}{\textcolor {Chapter }{Examples of Subdirect Products of Index Two}}{section.2.9}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.9.1}\textcolor {Chapter }{Certain Dihedral Groups as Subdirect Products of Index Two}}{150}{subsection.2.9.1}\protected@file@percent }
\newlabel{subsect:dihedralsubdir}{{2.9.1}{150}{\textcolor {Chapter }{Certain Dihedral Groups as Subdirect Products of Index Two}}{subsection.2.9.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.9.2}\textcolor {Chapter }{The Character Table of $(D_{10} \times HN).2 < M$ (June 2008)}}{151}{subsection.2.9.2}\protected@file@percent }
\newlabel{subsect:The Character Table of (D10xHN).2}{{2.9.2}{151}{\textcolor {Chapter }{The Character Table of $(D_{10} \times HN).2 < M$ (June 2008)}}{subsection.2.9.2}{}}
\@writefile{brf}{\backcite{CCN85}{{151}{2.9.2}{subsection.2.9.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.9.3}\textcolor {Chapter }{A Counterexample (August 2015)}}{152}{subsection.2.9.3}\protected@file@percent }
\newlabel{subsect:Counterexample}{{2.9.3}{152}{\textcolor {Chapter }{A Counterexample (August 2015)}}{subsection.2.9.3}{}}
\citation{GAP}
\citation{CTblLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Constructing Character Tables of Central Extensions in \textsf  {GAP}}}{154}{chapter.3}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:CCE}{{3}{154}{\textcolor {Chapter }{Constructing Character Tables of Central Extensions in \textsf {GAP}}}{chapter.3}{}}
\@writefile{brf}{\backcite{GAP}{{154}{3}{chapter.3}}}
\@writefile{brf}{\backcite{CTblLib}{{154}{3}{chapter.3}}}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Coprime Central Extensions}}{154}{section.3.1}\protected@file@percent }
\newlabel{cce}{{3.1}{154}{\textcolor {Chapter }{Coprime Central Extensions}}{section.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{The Character Table Head}}{154}{subsection.3.1.1}\protected@file@percent }
\newlabel{subsect:The Character Table Head}{{3.1.1}{154}{\textcolor {Chapter }{The Character Table Head}}{subsection.3.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}\textcolor {Chapter }{The Irreducible Characters}}{155}{subsection.3.1.2}\protected@file@percent }
\newlabel{subsect:The Irreducible Characters}{{3.1.2}{155}{\textcolor {Chapter }{The Irreducible Characters}}{subsection.3.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.3}\textcolor {Chapter }{Ordering of Conjugacy Classes}}{156}{subsection.3.1.3}\protected@file@percent }
\newlabel{classes}{{3.1.3}{156}{\textcolor {Chapter }{Ordering of Conjugacy Classes}}{subsection.3.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.4}\textcolor {Chapter }{Compatibility with Smaller Factor Groups}}{157}{subsection.3.1.4}\protected@file@percent }
\newlabel{compat}{{3.1.4}{157}{\textcolor {Chapter }{Compatibility with Smaller Factor Groups}}{subsection.3.1.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{Examples}}{158}{section.3.2}\protected@file@percent }
\newlabel{sect:Examples}{{3.2}{158}{\textcolor {Chapter }{Examples}}{section.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.1}\textcolor {Chapter }{Central Extensions of Simple \textsf  {Atlas} Groups}}{158}{subsection.3.2.1}\protected@file@percent }
\newlabel{12M22}{{3.2.1}{158}{\textcolor {Chapter }{Central Extensions of Simple \textsf {Atlas} Groups}}{subsection.3.2.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.2}\textcolor {Chapter }{Central Extensions of Other \textsf  {Atlas} Groups}}{160}{subsection.3.2.2}\protected@file@percent }
\newlabel{subsect:Central Extensions of Other ATLAS Groups}{{3.2.2}{160}{\textcolor {Chapter }{Central Extensions of Other \textsf {Atlas} Groups}}{subsection.3.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.3}\textcolor {Chapter }{Compatible Central Extensions of Maximal Subgroups}}{161}{subsection.3.2.3}\protected@file@percent }
\newlabel{subsect:Compatible Central Extensions of Maximal Subgroups}{{3.2.3}{161}{\textcolor {Chapter }{Compatible Central Extensions of Maximal Subgroups}}{subsection.3.2.3}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2.4}\textcolor {Chapter }{The \texttt  {2B} Centralizer in $3.Fi_{24}'$ (January 2004)}}{162}{subsection.3.2.4}\protected@file@percent }
\newlabel{3F3pN2B}{{3.2.4}{162}{\textcolor {Chapter }{The \texttt {2B} Centralizer in $3.Fi_{24}'$ (January 2004)}}{subsection.3.2.4}{}}
\@writefile{brf}{\backcite{CCN85}{{162}{3.2.4}{subsection.3.2.4}}}
\citation{GAP}
\citation{GMN}
\citation{NW12}
\citation{Wil10}
\citation{GMN}
\citation{CTblLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{\textsf  {GAP} Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups}}{164}{chapter.4}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:hamilcyc}{{4}{164}{\textcolor {Chapter }{\textsf {GAP} Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups}}{chapter.4}{}}
\@writefile{brf}{\backcite{GAP}{{164}{4}{chapter.4}}}
\@writefile{brf}{\backcite{GMN}{{164}{4}{chapter.4}}}
\@writefile{brf}{\backcite{NW12}{{164}{4}{chapter.4}}}
\@writefile{brf}{\backcite{Wil10}{{164}{4}{chapter.4}}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Overview}}{164}{section.4.1}\protected@file@percent }
\newlabel{sect:Overview}{{4.1}{164}{\textcolor {Chapter }{Overview}}{section.4.1}{}}
\@writefile{brf}{\backcite{GMN}{{164}{4.1}{section.4.1}}}
\citation{GMN}
\citation{GMN}
\citation{GMN}
\citation{BGK}
\citation{ProbGenArxiv}
\@writefile{brf}{\backcite{CTblLib}{{165}{4.1}{section.4.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}\textcolor {Chapter }{Theoretical Background}}{165}{section.4.2}\protected@file@percent }
\newlabel{background}{{4.2}{165}{\textcolor {Chapter }{Theoretical Background}}{section.4.2}{}}
\@writefile{brf}{\backcite{GMN}{{165}{4.2}{section.4.2}}}
\@writefile{brf}{\backcite{GMN}{{165}{4.2}{section.4.2}}}
\@writefile{brf}{\backcite{GMN}{{165}{4.2}{section.4.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}\textcolor {Chapter }{Character-Theoretic Lower Bounds for Vertex Degrees}}{166}{subsection.4.2.1}\protected@file@percent }
\newlabel{sect:Character-Theoretic Lower Bounds for Vertex Degrees}{{4.2.1}{166}{\textcolor {Chapter }{Character-Theoretic Lower Bounds for Vertex Degrees}}{subsection.4.2.1}{}}
\@writefile{brf}{\backcite{BGK}{{166}{4.2.1}{subsection.4.2.1}}}
\@writefile{brf}{\backcite{ProbGenArxiv}{{166}{4.2.1}{subsection.4.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}\textcolor {Chapter }{Checking the Criteria}}{167}{subsection.4.2.2}\protected@file@percent }
\newlabel{critcheck}{{4.2.2}{167}{\textcolor {Chapter }{Checking the Criteria}}{subsection.4.2.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}\textcolor {Chapter }{\textsf  {GAP} Functions for the Computations}}{167}{section.4.3}\protected@file@percent }
\newlabel{functions}{{4.3}{167}{\textcolor {Chapter }{\textsf {GAP} Functions for the Computations}}{section.4.3}{}}
\citation{ProbGenArxiv}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}\textcolor {Chapter }{Computing Vertex Degrees from the Group}}{168}{subsection.4.3.1}\protected@file@percent }
\newlabel{groups}{{4.3.1}{168}{\textcolor {Chapter }{Computing Vertex Degrees from the Group}}{subsection.4.3.1}{}}
\@writefile{brf}{\backcite{ProbGenArxiv}{{168}{4.3.1}{subsection.4.3.1}}}
\citation{ProbGenArxiv}
\citation{CTblLib}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.2}\textcolor {Chapter }{Computing Lower Bounds for Vertex Degrees}}{170}{subsection.4.3.2}\protected@file@percent }
\newlabel{characters}{{4.3.2}{170}{\textcolor {Chapter }{Computing Lower Bounds for Vertex Degrees}}{subsection.4.3.2}{}}
\@writefile{brf}{\backcite{ProbGenArxiv}{{170}{4.3.2}{subsection.4.3.2}}}
\@writefile{brf}{\backcite{CTblLib}{{170}{4.3.2}{subsection.4.3.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.3}\textcolor {Chapter }{Evaluating the (Lower Bounds for the) Vertex Degrees}}{172}{subsection.4.3.3}\protected@file@percent }
\newlabel{clos}{{4.3.3}{172}{\textcolor {Chapter }{Evaluating the (Lower Bounds for the) Vertex Degrees}}{subsection.4.3.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.4}\textcolor {Chapter }{Character-Theoretic Computations}}{174}{section.4.4}\protected@file@percent }
\newlabel{chartheor}{{4.4}{174}{\textcolor {Chapter }{Character-Theoretic Computations}}{section.4.4}{}}
\citation{NW12}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}\textcolor {Chapter }{Sporadic Simple Groups, except the Monster}}{175}{subsection.4.4.1}\protected@file@percent }
\newlabel{spor}{{4.4.1}{175}{\textcolor {Chapter }{Sporadic Simple Groups, except the Monster}}{subsection.4.4.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.2}\textcolor {Chapter }{The Monster}}{175}{subsection.4.4.2}\protected@file@percent }
\newlabel{Monster}{{4.4.2}{175}{\textcolor {Chapter }{The Monster}}{subsection.4.4.2}{}}
\@writefile{brf}{\backcite{NW12}{{175}{4.4.2}{subsection.4.4.2}}}
\citation{NW12}
\@writefile{brf}{\backcite{NW12}{{176}{4.4.2}{subsection.4.4.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.3}\textcolor {Chapter }{Nonsimple Automorphism Groups of Sporadic Simple Groups}}{178}{subsection.4.4.3}\protected@file@percent }
\newlabel{sporaut}{{4.4.3}{178}{\textcolor {Chapter }{Nonsimple Automorphism Groups of Sporadic Simple Groups}}{subsection.4.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.4}\textcolor {Chapter }{Alternating and Symmetric Groups $A_n$, $S_n$, for $5 \leq n \leq 13$}}{179}{subsection.4.4.4}\protected@file@percent }
\newlabel{symmalt}{{4.4.4}{179}{\textcolor {Chapter }{Alternating and Symmetric Groups $A_n$, $S_n$, for $5 \leq n \leq 13$}}{subsection.4.4.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4.5}\textcolor {Chapter }{Computations With Groups}}{179}{section.4.5}\protected@file@percent }
\newlabel{grouptheor}{{4.5}{179}{\textcolor {Chapter }{Computations With Groups}}{section.4.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5.1}\textcolor {Chapter }{Nonabelian Simple Groups of Order up to $10^7$}}{180}{subsection.4.5.1}\protected@file@percent }
\newlabel{smallsimp}{{4.5.1}{180}{\textcolor {Chapter }{Nonabelian Simple Groups of Order up to $10^7$}}{subsection.4.5.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5.2}\textcolor {Chapter }{Nonsimple Groups with Nonsolvable Socle of Order at most $10^6$}}{182}{subsection.4.5.2}\protected@file@percent }
\newlabel{smallalmostsimple}{{4.5.2}{182}{\textcolor {Chapter }{Nonsimple Groups with Nonsolvable Socle of Order at most $10^6$}}{subsection.4.5.2}{}}
\citation{Hup67}
\@writefile{toc}{\contentsline {section}{\numberline {4.6}\textcolor {Chapter }{The Groups ${{\rm  PSL}}(2,q)$}}{184}{section.4.6}\protected@file@percent }
\newlabel{psl2q}{{4.6}{184}{\textcolor {Chapter }{The Groups ${{\rm PSL}}(2,q)$}}{section.4.6}{}}
\@writefile{brf}{\backcite{Hup67}{{185}{4.6}{section.4.6}}}
\citation{BGS11}
\citation{Kle87}
\citation{CCN85}
\citation{BGS11}
\@writefile{toc}{\contentsline {chapter}{\numberline {5}\textcolor {Chapter }{\textsf  {GAP} Computations with $O_8^+(5).S_3$ and $O_8^+(2).S_3$}}{188}{chapter.5}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:o8p2s3_o8p5s3}{{5}{188}{\textcolor {Chapter }{\textsf {GAP} Computations with $O_8^+(5).S_3$ and $O_8^+(2).S_3$}}{chapter.5}{}}
\@writefile{brf}{\backcite{BGS11}{{188}{5}{chapter.5}}}
\@writefile{toc}{\contentsline {section}{\numberline {5.1}\textcolor {Chapter }{Overview}}{188}{section.5.1}\protected@file@percent }
\newlabel{sect:overview_o8p2s3}{{5.1}{188}{\textcolor {Chapter }{Overview}}{section.5.1}{}}
\@writefile{brf}{\backcite{Kle87}{{188}{5.1}{section.5.1}}}
\@writefile{brf}{\backcite{CCN85}{{188}{5.1}{section.5.1}}}
\citation{CCN85}
\@writefile{brf}{\backcite{BGS11}{{189}{5.1}{section.5.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {5.2}\textcolor {Chapter }{Constructing Representations of $M.2$ and $S.2$}}{189}{section.5.2}\protected@file@percent }
\newlabel{sect:sect2}{{5.2}{189}{\textcolor {Chapter }{Constructing Representations of $M.2$ and $S.2$}}{section.5.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}\textcolor {Chapter }{A Matrix Representation of the Weyl Group of Type $E_8$}}{189}{subsection.5.2.1}\protected@file@percent }
\newlabel{subsect:repres_W_E8}{{5.2.1}{189}{\textcolor {Chapter }{A Matrix Representation of the Weyl Group of Type $E_8$}}{subsection.5.2.1}{}}
\@writefile{brf}{\backcite{CCN85}{{189}{5.2.1}{subsection.5.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.2}\textcolor {Chapter }{Embedding the Weyl group of Type $E_8$ into GO${}^+(8,5)$}}{189}{subsection.5.2.2}\protected@file@percent }
\newlabel{subsect:embedding_W_E8}{{5.2.2}{189}{\textcolor {Chapter }{Embedding the Weyl group of Type $E_8$ into GO${}^+(8,5)$}}{subsection.5.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.3}\textcolor {Chapter }{Compatible Generators of $M$, $M.2$, $S$, and $S.2$}}{190}{subsection.5.2.3}\protected@file@percent }
\newlabel{subsect:120pt}{{5.2.3}{190}{\textcolor {Chapter }{Compatible Generators of $M$, $M.2$, $S$, and $S.2$}}{subsection.5.2.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.3}\textcolor {Chapter }{Constructing Representations of $M.3$ and $S.3$}}{191}{section.5.3}\protected@file@percent }
\newlabel{sect:sect3}{{5.3}{191}{\textcolor {Chapter }{Constructing Representations of $M.3$ and $S.3$}}{section.5.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3.1}\textcolor {Chapter }{The Action of $M.3$ on $M$}}{191}{subsection.5.3.1}\protected@file@percent }
\newlabel{sect:action_M.3_M}{{5.3.1}{191}{\textcolor {Chapter }{The Action of $M.3$ on $M$}}{subsection.5.3.1}{}}
\citation{Kle87}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3.2}\textcolor {Chapter }{The Action of $S.3$ on $S$}}{192}{subsection.5.3.2}\protected@file@percent }
\newlabel{subsect:M.3andS.3}{{5.3.2}{192}{\textcolor {Chapter }{The Action of $S.3$ on $S$}}{subsection.5.3.2}{}}
\@writefile{brf}{\backcite{Kle87}{{192}{5.3.2}{subsection.5.3.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {5.4}\textcolor {Chapter }{Constructing Compatible Generators of $H$ and $G$}}{194}{section.5.4}\protected@file@percent }
\newlabel{sect:sect4}{{5.4}{194}{\textcolor {Chapter }{Constructing Compatible Generators of $H$ and $G$}}{section.5.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.5}\textcolor {Chapter }{Application: Regular Orbits of $H$ on $G/H$}}{194}{section.5.5}\protected@file@percent }
\newlabel{sect:appl}{{5.5}{194}{\textcolor {Chapter }{Application: Regular Orbits of $H$ on $G/H$}}{section.5.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.6}\textcolor {Chapter }{Appendix: The Permutation Character $(1_H^G)_H$}}{195}{section.5.6}\protected@file@percent }
\newlabel{sect:appendix_permchar}{{5.6}{195}{\textcolor {Chapter }{Appendix: The Permutation Character $(1_H^G)_H$}}{section.5.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5.7}\textcolor {Chapter }{Appendix: The Data File}}{198}{section.5.7}\protected@file@percent }
\newlabel{sect:appendix_data}{{5.7}{198}{\textcolor {Chapter }{Appendix: The Data File}}{section.5.7}{}}
\citation{CCN85}
\citation{GAP}
\citation{CTblLib}
\citation{TomLib}
\citation{NW12}
\citation{Wil10}
\citation{CCN85}
\@writefile{toc}{\contentsline {chapter}{\numberline {6}\textcolor {Chapter }{Solvable Subgroups of Maximal Order in Sporadic Simple Groups}}{200}{chapter.6}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:sporsolv}{{6}{200}{\textcolor {Chapter }{Solvable Subgroups of Maximal Order in Sporadic Simple Groups}}{chapter.6}{}}
\@writefile{brf}{\backcite{CCN85}{{200}{6}{chapter.6}}}
\@writefile{brf}{\backcite{GAP}{{200}{6}{chapter.6}}}
\@writefile{brf}{\backcite{CTblLib}{{200}{6}{chapter.6}}}
\@writefile{brf}{\backcite{TomLib}{{200}{6}{chapter.6}}}
\@writefile{brf}{\backcite{NW12}{{200}{6}{chapter.6}}}
\@writefile{brf}{\backcite{Wil10}{{200}{6}{chapter.6}}}
\@writefile{toc}{\contentsline {section}{\numberline {6.1}\textcolor {Chapter }{The Result}}{200}{section.6.1}\protected@file@percent }
\newlabel{sect:result}{{6.1}{200}{\textcolor {Chapter }{The Result}}{section.6.1}{}}
\@writefile{brf}{\backcite{CCN85}{{200}{6.1}{section.6.1}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{201}{6.1}{section.6.1}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{203}{6.1}{section.6.1}}}
\citation{CCN85}
\citation{CCN85}
\citation{GAP}
\citation{CTblLib}
\citation{TomLib}
\citation{TomLib}
\@writefile{brf}{\backcite{CCN85}{{204}{6.1}{section.6.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {6.2}\textcolor {Chapter }{The Approach}}{204}{section.6.2}\protected@file@percent }
\newlabel{sect:approach}{{6.2}{204}{\textcolor {Chapter }{The Approach}}{section.6.2}{}}
\@writefile{brf}{\backcite{CCN85}{{204}{6.2}{section.6.2}}}
\@writefile{brf}{\backcite{GAP}{{204}{6.2}{section.6.2}}}
\@writefile{brf}{\backcite{CTblLib}{{204}{6.2}{section.6.2}}}
\@writefile{brf}{\backcite{TomLib}{{204}{6.2}{section.6.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.1}\textcolor {Chapter }{Use the Table of Marks}}{204}{subsection.6.2.1}\protected@file@percent }
\newlabel{sect:Use the Table of Marks}{{6.2.1}{204}{\textcolor {Chapter }{Use the Table of Marks}}{subsection.6.2.1}{}}
\@writefile{brf}{\backcite{TomLib}{{204}{6.2.1}{subsection.6.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.2}\textcolor {Chapter }{Use Information from the Character Table Library}}{205}{subsection.6.2.2}\protected@file@percent }
\newlabel{sect:Use Information from the Character Table Library}{{6.2.2}{205}{\textcolor {Chapter }{Use Information from the Character Table Library}}{subsection.6.2.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6.3}\textcolor {Chapter }{Cases where the Table of Marks is available in \textsf  {GAP}}}{206}{section.6.3}\protected@file@percent }
\newlabel{sect:EASY}{{6.3}{206}{\textcolor {Chapter }{Cases where the Table of Marks is available in \textsf {GAP}}}{section.6.3}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{BN95}
\@writefile{brf}{\backcite{CCN85}{{207}{6.3}{section.6.3}}}
\@writefile{brf}{\backcite{CCN85}{{207}{6.3}{section.6.3}}}
\@writefile{brf}{\backcite{CCN85}{{207}{6.3}{section.6.3}}}
\@writefile{brf}{\backcite{BN95}{{207}{6.3}{section.6.3}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {6.4}\textcolor {Chapter }{Cases where the Table of Marks is not available in \textsf  {GAP}}}{208}{section.6.4}\protected@file@percent }
\newlabel{sect:Cases where the Table of Marks is not available in GAP}{{6.4}{208}{\textcolor {Chapter }{Cases where the Table of Marks is not available in \textsf {GAP}}}{section.6.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.1}\textcolor {Chapter }{$G = Ru$}}{208}{subsection.6.4.1}\protected@file@percent }
\newlabel{sect:Ru}{{6.4.1}{208}{\textcolor {Chapter }{$G = Ru$}}{subsection.6.4.1}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.1}{subsection.6.4.1}}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.1}{subsection.6.4.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.2}\textcolor {Chapter }{$G = Suz$}}{209}{subsection.6.4.2}\protected@file@percent }
\newlabel{sect:Suz}{{6.4.2}{209}{\textcolor {Chapter }{$G = Suz$}}{subsection.6.4.2}{}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.2}{subsection.6.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.2}{subsection.6.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.2}{subsection.6.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.2}{subsection.6.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{209}{6.4.2}{subsection.6.4.2}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.3}\textcolor {Chapter }{$G = ON$}}{210}{subsection.6.4.3}\protected@file@percent }
\newlabel{sect:ON}{{6.4.3}{210}{\textcolor {Chapter }{$G = ON$}}{subsection.6.4.3}{}}
\@writefile{brf}{\backcite{CCN85}{{210}{6.4.3}{subsection.6.4.3}}}
\@writefile{brf}{\backcite{CCN85}{{210}{6.4.3}{subsection.6.4.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.4}\textcolor {Chapter }{$G = Co_2$}}{210}{subsection.6.4.4}\protected@file@percent }
\newlabel{sect:Co2}{{6.4.4}{210}{\textcolor {Chapter }{$G = Co_2$}}{subsection.6.4.4}{}}
\@writefile{brf}{\backcite{CCN85}{{210}{6.4.4}{subsection.6.4.4}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.4}{subsection.6.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.4}{subsection.6.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.4}{subsection.6.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.4}{subsection.6.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.4}{subsection.6.4.4}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.5}\textcolor {Chapter }{$G = Fi_{22}$}}{211}{subsection.6.4.5}\protected@file@percent }
\newlabel{sect:Fi22}{{6.4.5}{211}{\textcolor {Chapter }{$G = Fi_{22}$}}{subsection.6.4.5}{}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.5}{subsection.6.4.5}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.5}{subsection.6.4.5}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.5}{subsection.6.4.5}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.5}{subsection.6.4.5}}}
\@writefile{brf}{\backcite{CCN85}{{211}{6.4.5}{subsection.6.4.5}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.6}\textcolor {Chapter }{$G = HN$}}{212}{subsection.6.4.6}\protected@file@percent }
\newlabel{sect:HN}{{6.4.6}{212}{\textcolor {Chapter }{$G = HN$}}{subsection.6.4.6}{}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.6}{subsection.6.4.6}}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.6}{subsection.6.4.6}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.7}\textcolor {Chapter }{$G = Ly$}}{212}{subsection.6.4.7}\protected@file@percent }
\newlabel{sect:Ly}{{6.4.7}{212}{\textcolor {Chapter }{$G = Ly$}}{subsection.6.4.7}{}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.7}{subsection.6.4.7}}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.7}{subsection.6.4.7}}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.7}{subsection.6.4.7}}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.7}{subsection.6.4.7}}}
\@writefile{brf}{\backcite{CCN85}{{212}{6.4.7}{subsection.6.4.7}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.8}\textcolor {Chapter }{$G = Th$}}{213}{subsection.6.4.8}\protected@file@percent }
\newlabel{sect:Th}{{6.4.8}{213}{\textcolor {Chapter }{$G = Th$}}{subsection.6.4.8}{}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.8}{subsection.6.4.8}}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.8}{subsection.6.4.8}}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.8}{subsection.6.4.8}}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.8}{subsection.6.4.8}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.9}\textcolor {Chapter }{$G = Fi_{23}$}}{213}{subsection.6.4.9}\protected@file@percent }
\newlabel{sect:Fi23}{{6.4.9}{213}{\textcolor {Chapter }{$G = Fi_{23}$}}{subsection.6.4.9}{}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.9}{subsection.6.4.9}}}
\@writefile{brf}{\backcite{CCN85}{{213}{6.4.9}{subsection.6.4.9}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.10}\textcolor {Chapter }{$G = Co_1$}}{214}{subsection.6.4.10}\protected@file@percent }
\newlabel{sect:Co1}{{6.4.10}{214}{\textcolor {Chapter }{$G = Co_1$}}{subsection.6.4.10}{}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.10}{subsection.6.4.10}}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.10}{subsection.6.4.10}}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.10}{subsection.6.4.10}}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.10}{subsection.6.4.10}}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.10}{subsection.6.4.10}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.11}\textcolor {Chapter }{$G = J_4$}}{214}{subsection.6.4.11}\protected@file@percent }
\newlabel{sect:J4}{{6.4.11}{214}{\textcolor {Chapter }{$G = J_4$}}{subsection.6.4.11}{}}
\@writefile{brf}{\backcite{CCN85}{{214}{6.4.11}{subsection.6.4.11}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{215}{6.4.11}{subsection.6.4.11}}}
\@writefile{brf}{\backcite{CCN85}{{215}{6.4.11}{subsection.6.4.11}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.12}\textcolor {Chapter }{$G = Fi_{24}^{\prime }$}}{215}{subsection.6.4.12}\protected@file@percent }
\newlabel{sect:F3+}{{6.4.12}{215}{\textcolor {Chapter }{$G = Fi_{24}^{\prime }$}}{subsection.6.4.12}{}}
\@writefile{brf}{\backcite{CCN85}{{215}{6.4.12}{subsection.6.4.12}}}
\citation{CCN85}
\citation{Wil99}
\@writefile{brf}{\backcite{CCN85}{{216}{6.4.12}{subsection.6.4.12}}}
\@writefile{brf}{\backcite{CCN85}{{216}{6.4.12}{subsection.6.4.12}}}
\@writefile{brf}{\backcite{CCN85}{{216}{6.4.12}{subsection.6.4.12}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.13}\textcolor {Chapter }{$G = B$}}{216}{subsection.6.4.13}\protected@file@percent }
\newlabel{sect:B}{{6.4.13}{216}{\textcolor {Chapter }{$G = B$}}{subsection.6.4.13}{}}
\@writefile{brf}{\backcite{CCN85}{{216}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{Wil99}{{216}{6.4.13}{subsection.6.4.13}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\citation{BN95}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{BN95}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{217}{6.4.13}{subsection.6.4.13}}}
\@writefile{brf}{\backcite{CCN85}{{218}{6.4.13}{subsection.6.4.13}}}
\citation{AtlasRep}
\citation{CCN85}
\@writefile{brf}{\backcite{AtlasRep}{{220}{6.4.13}{subsection.6.4.13}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.14}\textcolor {Chapter }{$G = M$}}{220}{subsection.6.4.14}\protected@file@percent }
\newlabel{sect:M}{{6.4.14}{220}{\textcolor {Chapter }{$G = M$}}{subsection.6.4.14}{}}
\@writefile{brf}{\backcite{CCN85}{{220}{6.4.14}{subsection.6.4.14}}}
\citation{NW12}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{NW12}{{221}{6.4.14}{subsection.6.4.14}}}
\@writefile{brf}{\backcite{CCN85}{{221}{6.4.14}{subsection.6.4.14}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{222}{6.4.14}{subsection.6.4.14}}}
\@writefile{brf}{\backcite{CCN85}{{222}{6.4.14}{subsection.6.4.14}}}
\@writefile{brf}{\backcite{CCN85}{{222}{6.4.14}{subsection.6.4.14}}}
\citation{CCN85}
\citation{AtlasRep}
\@writefile{brf}{\backcite{CCN85}{{223}{6.4.14}{Item.10}}}
\@writefile{brf}{\backcite{AtlasRep}{{224}{6.4.14}{Item.10}}}
\@writefile{toc}{\contentsline {section}{\numberline {6.5}\textcolor {Chapter }{Proof of the Corollary}}{225}{section.6.5}\protected@file@percent }
\newlabel{sect:corollary}{{6.5}{225}{\textcolor {Chapter }{Proof of the Corollary}}{section.6.5}{}}
\citation{CCN85}
\citation{GAP}
\citation{CTblLib}
\citation{TomLib}
\citation{Vdo00}
\@writefile{toc}{\contentsline {chapter}{\numberline {7}\textcolor {Chapter }{Large Nilpotent Subgroups of Sporadic Simple Groups}}{226}{chapter.7}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:spornilp}{{7}{226}{\textcolor {Chapter }{Large Nilpotent Subgroups of Sporadic Simple Groups}}{chapter.7}{}}
\@writefile{brf}{\backcite{CCN85}{{226}{7}{chapter.7}}}
\@writefile{brf}{\backcite{GAP}{{226}{7}{chapter.7}}}
\@writefile{brf}{\backcite{CTblLib}{{226}{7}{chapter.7}}}
\@writefile{brf}{\backcite{TomLib}{{226}{7}{chapter.7}}}
\@writefile{brf}{\backcite{Vdo00}{{226}{7}{chapter.7}}}
\@writefile{toc}{\contentsline {section}{\numberline {7.1}\textcolor {Chapter }{The Result}}{226}{section.7.1}\protected@file@percent }
\newlabel{sect:spornilp_result}{{7.1}{226}{\textcolor {Chapter }{The Result}}{section.7.1}{}}
\citation{CCN85}
\citation{CCN85}
\citation{Mmaxes}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{227}{7.1}{section.7.1}}}
\@writefile{brf}{\backcite{CCN85}{{227}{7.1}{section.7.1}}}
\@writefile{brf}{\backcite{Mmaxes}{{227}{7.1}{section.7.1}}}
\@writefile{brf}{\backcite{CCN85}{{227}{7.1}{section.7.1}}}
\@writefile{brf}{\backcite{CCN85}{{228}{7.1}{section.7.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {7.2}\textcolor {Chapter }{The Proof}}{228}{section.7.2}\protected@file@percent }
\newlabel{sect:The Proof}{{7.2}{228}{\textcolor {Chapter }{The Proof}}{section.7.2}{}}
\citation{CCN85}
\citation{BN95}
\citation{CTblLib}
\@writefile{brf}{\backcite{CCN85}{{229}{7.2}{section.7.2}}}
\@writefile{brf}{\backcite{BN95}{{229}{7.2}{section.7.2}}}
\@writefile{brf}{\backcite{CTblLib}{{230}{7.2}{section.7.2}}}
\citation{TomLib}
\@writefile{toc}{\contentsline {section}{\numberline {7.3}\textcolor {Chapter }{Alternative: Use \textsf  {GAP}'s Tables of Marks}}{231}{section.7.3}\protected@file@percent }
\newlabel{sect:Alternative_Use_TOM}{{7.3}{231}{\textcolor {Chapter }{Alternative: Use \textsf {GAP}'s Tables of Marks}}{section.7.3}{}}
\@writefile{brf}{\backcite{TomLib}{{231}{7.3}{section.7.3}}}
\citation{GAP}
\citation{BP98copy}
\citation{CCN85}
\citation{CTblLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {8}\textcolor {Chapter }{Permutation Characters in \textsf  {GAP}}}{234}{chapter.8}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:ctblpope}{{8}{234}{\textcolor {Chapter }{Permutation Characters in \textsf {GAP}}}{chapter.8}{}}
\@writefile{brf}{\backcite{GAP}{{234}{8}{chapter.8}}}
\@writefile{brf}{\backcite{BP98copy}{{234}{8}{chapter.8}}}
\@writefile{brf}{\backcite{CCN85}{{234}{8}{chapter.8}}}
\@writefile{brf}{\backcite{CTblLib}{{234}{8}{chapter.8}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.1}\textcolor {Chapter }{Some Computations with $M_{24}$}}{234}{section.8.1}\protected@file@percent }
\newlabel{sect:comp_M24}{{8.1}{234}{\textcolor {Chapter }{Some Computations with $M_{24}$}}{section.8.1}{}}
\citation{BP98copy}
\@writefile{toc}{\contentsline {section}{\numberline {8.2}\textcolor {Chapter }{All Possible Permutation Characters of $M_{11}$}}{237}{section.8.2}\protected@file@percent }
\newlabel{sect:poss_perm_char_M11}{{8.2}{237}{\textcolor {Chapter }{All Possible Permutation Characters of $M_{11}$}}{section.8.2}{}}
\@writefile{brf}{\backcite{BP98copy}{{237}{8.2}{section.8.2}}}
\citation{BP98copy}
\citation{BP98copy}
\@writefile{brf}{\backcite{BP98copy}{{238}{8.2}{section.8.2}}}
\@writefile{brf}{\backcite{BP98copy}{{238}{8.2}{section.8.2}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.3}\textcolor {Chapter }{The Action of $U_6(2)$ on the Cosets of $M_{22}$}}{239}{section.8.3}\protected@file@percent }
\newlabel{sect:act_U62_M22}{{8.3}{239}{\textcolor {Chapter }{The Action of $U_6(2)$ on the Cosets of $M_{22}$}}{section.8.3}{}}
\@writefile{brf}{\backcite{CCN85}{{239}{8.3}{section.8.3}}}
\@writefile{brf}{\backcite{CCN85}{{239}{8.3}{section.8.3}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{240}{8.3}{section.8.3}}}
\@writefile{brf}{\backcite{CCN85}{{240}{8.3}{section.8.3}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.4}\textcolor {Chapter }{Degree $20\,736$ Permutation Characters of $U_6(2)$}}{241}{section.8.4}\protected@file@percent }
\newlabel{sect:deg_20736_U62}{{8.4}{241}{\textcolor {Chapter }{Degree $20\,736$ Permutation Characters of $U_6(2)$}}{section.8.4}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.5}\textcolor {Chapter }{Degree $57\,572\,775$ Permutation Characters of $O_8^+(3)$}}{242}{section.8.5}\protected@file@percent }
\newlabel{sect:degree_57572775_O8p3}{{8.5}{242}{\textcolor {Chapter }{Degree $57\,572\,775$ Permutation Characters of $O_8^+(3)$}}{section.8.5}{}}
\@writefile{brf}{\backcite{CCN85}{{242}{8.5}{section.8.5}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.6}\textcolor {Chapter }{The Action of $O_7(3).2$ on the Cosets of $2^7.S_7$}}{243}{section.8.6}\protected@file@percent }
\newlabel{sect:action_O73d2_27S7}{{8.6}{243}{\textcolor {Chapter }{The Action of $O_7(3).2$ on the Cosets of $2^7.S_7$}}{section.8.6}{}}
\@writefile{brf}{\backcite{CCN85}{{243}{8.6}{section.8.6}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.7}\textcolor {Chapter }{The Action of $O_8^+(3).2_1$ on the Cosets of $2^7.A_8$}}{245}{section.8.7}\protected@file@percent }
\newlabel{sect:action_O8p3d2a_27A8}{{8.7}{245}{\textcolor {Chapter }{The Action of $O_8^+(3).2_1$ on the Cosets of $2^7.A_8$}}{section.8.7}{}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.8}\textcolor {Chapter }{The Action of $S_4(4).4$ on the Cosets of $5^2.[2^5]$}}{248}{section.8.8}\protected@file@percent }
\newlabel{sect:action_S44d4_5225}{{8.8}{248}{\textcolor {Chapter }{The Action of $S_4(4).4$ on the Cosets of $5^2.[2^5]$}}{section.8.8}{}}
\@writefile{brf}{\backcite{CCN85}{{248}{8.8}{section.8.8}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.9}\textcolor {Chapter }{The Action of $Co_1$ on the Cosets of Involution Centralizers}}{248}{section.8.9}\protected@file@percent }
\newlabel{sect:action_Co1_inv_centralizers}{{8.9}{248}{\textcolor {Chapter }{The Action of $Co_1$ on the Cosets of Involution Centralizers}}{section.8.9}{}}
\@writefile{brf}{\backcite{CCN85}{{248}{8.9}{section.8.9}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.10}\textcolor {Chapter }{The Multiplicity Free Permutation Characters of $G_2(3)$}}{251}{section.8.10}\protected@file@percent }
\newlabel{sect:multfree_G23}{{8.10}{251}{\textcolor {Chapter }{The Multiplicity Free Permutation Characters of $G_2(3)$}}{section.8.10}{}}
\@writefile{brf}{\backcite{CCN85}{{251}{8.10}{section.8.10}}}
\@writefile{brf}{\backcite{CCN85}{{251}{8.10}{section.8.10}}}
\citation{CCN85}
\citation{CCN85}
\citation{Isa76}
\@writefile{toc}{\contentsline {section}{\numberline {8.11}\textcolor {Chapter }{Degree $11\,200$ Permutation Characters of $O_8^+(2)$}}{252}{section.8.11}\protected@file@percent }
\newlabel{sect:degree_11200_O8p2}{{8.11}{252}{\textcolor {Chapter }{Degree $11\,200$ Permutation Characters of $O_8^+(2)$}}{section.8.11}{}}
\@writefile{brf}{\backcite{CCN85}{{252}{8.11}{section.8.11}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.12}\textcolor {Chapter }{A Proof of Nonexistence of a Certain Subgroup}}{253}{section.8.12}\protected@file@percent }
\newlabel{sect:proof_nonexistence}{{8.12}{253}{\textcolor {Chapter }{A Proof of Nonexistence of a Certain Subgroup}}{section.8.12}{}}
\@writefile{brf}{\backcite{CCN85}{{253}{8.12}{section.8.12}}}
\@writefile{brf}{\backcite{Isa76}{{253}{8.12}{section.8.12}}}
\citation{Hup67}
\citation{BP98copy}
\citation{CCN85}
\citation{CCN85}
\citation{BP98copy}
\citation{BP98copy}
\citation{BP98copy}
\@writefile{brf}{\backcite{Hup67}{{255}{8.12}{section.8.12}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.13}\textcolor {Chapter }{A Permutation Character of the Lyons group}}{255}{section.8.13}\protected@file@percent }
\newlabel{sect:character_Lyons}{{8.13}{255}{\textcolor {Chapter }{A Permutation Character of the Lyons group}}{section.8.13}{}}
\@writefile{brf}{\backcite{BP98copy}{{255}{8.13}{section.8.13}}}
\@writefile{brf}{\backcite{CCN85}{{255}{8.13}{section.8.13}}}
\@writefile{brf}{\backcite{CCN85}{{255}{8.13}{section.8.13}}}
\@writefile{brf}{\backcite{BP98copy}{{255}{8.13}{section.8.13}}}
\@writefile{brf}{\backcite{BP98copy}{{255}{8.13}{section.8.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{BP98copy}{{256}{8.13}{section.8.13}}}
\@writefile{brf}{\backcite{CCN85}{{256}{8.13}{section.8.13}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{257}{8.13}{section.8.13}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.14}\textcolor {Chapter }{Identifying two subgroups of Aut$(U_3(5))$ (October{\nobreakspace  }2001)}}{257}{section.8.14}\protected@file@percent }
\newlabel{sect:U35sub}{{8.14}{257}{\textcolor {Chapter }{Identifying two subgroups of Aut$(U_3(5))$ (October{\nobreakspace }2001)}}{section.8.14}{}}
\@writefile{brf}{\backcite{CCN85}{{257}{8.14}{section.8.14}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.15}\textcolor {Chapter }{A Permutation Character of Aut$(O_8^+(2))$ (October{\nobreakspace  }2001)}}{259}{section.8.15}\protected@file@percent }
\newlabel{sect:O82sub}{{8.15}{259}{\textcolor {Chapter }{A Permutation Character of Aut$(O_8^+(2))$ (October{\nobreakspace }2001)}}{section.8.15}{}}
\@writefile{brf}{\backcite{CCN85}{{259}{8.15}{section.8.15}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {8.16}\textcolor {Chapter }{Four Primitive Permutation Characters of the Monster Group}}{260}{section.8.16}\protected@file@percent }
\newlabel{sect:monsterperm}{{8.16}{260}{\textcolor {Chapter }{Four Primitive Permutation Characters of the Monster Group}}{section.8.16}{}}
\@writefile{brf}{\backcite{CCN85}{{260}{8.16}{section.8.16}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.16.1}\textcolor {Chapter }{The Subgroup $2^2.2^{11}.2^{22}.(S_3 \times M_{24})$ (June{\nobreakspace  }2009)}}{261}{subsection.8.16.1}\protected@file@percent }
\newlabel{subsect:monsterperm1}{{8.16.1}{261}{\textcolor {Chapter }{The Subgroup $2^2.2^{11}.2^{22}.(S_3 \times M_{24})$ (June{\nobreakspace }2009)}}{subsection.8.16.1}{}}
\@writefile{brf}{\backcite{CCN85}{{261}{8.16.1}{subsection.8.16.1}}}
\@writefile{brf}{\backcite{CCN85}{{261}{8.16.1}{subsection.8.16.1}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.16.2}\textcolor {Chapter }{The Subgroup $2^3.2^6.2^{12}.2^{18}.(L_3(2) \times 3.S_6)$ (September{\nobreakspace  }2009)}}{263}{subsection.8.16.2}\protected@file@percent }
\newlabel{subsect:monsterperm2}{{8.16.2}{263}{\textcolor {Chapter }{The Subgroup $2^3.2^6.2^{12}.2^{18}.(L_3(2) \times 3.S_6)$ (September{\nobreakspace }2009)}}{subsection.8.16.2}{}}
\@writefile{brf}{\backcite{CCN85}{{263}{8.16.2}{subsection.8.16.2}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{264}{8.16.2}{subsection.8.16.2}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.16.3}\textcolor {Chapter }{The Subgroup $2^5.2^{10}.2^{20}.(S_3 \times L_5(2))$ (October{\nobreakspace  }2009)}}{268}{subsection.8.16.3}\protected@file@percent }
\newlabel{subsect:monsterperm3}{{8.16.3}{268}{\textcolor {Chapter }{The Subgroup $2^5.2^{10}.2^{20}.(S_3 \times L_5(2))$ (October{\nobreakspace }2009)}}{subsection.8.16.3}{}}
\@writefile{brf}{\backcite{CCN85}{{268}{8.16.3}{subsection.8.16.3}}}
\@writefile{brf}{\backcite{CCN85}{{268}{8.16.3}{subsection.8.16.3}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {8.16.4}\textcolor {Chapter }{The Subgroup $2^{{10+16}}.O_{10}^+(2)$ (November{\nobreakspace  }2009)}}{272}{subsection.8.16.4}\protected@file@percent }
\newlabel{subsect:monsterperm4}{{8.16.4}{272}{\textcolor {Chapter }{The Subgroup $2^{{10+16}}.O_{10}^+(2)$ (November{\nobreakspace }2009)}}{subsection.8.16.4}{}}
\@writefile{brf}{\backcite{CCN85}{{272}{8.16.4}{subsection.8.16.4}}}
\@writefile{toc}{\contentsline {section}{\numberline {8.17}\textcolor {Chapter }{A permutation character of the Baby Monster (June{\nobreakspace  }2012)}}{278}{section.8.17}\protected@file@percent }
\newlabel{sect:comp_B}{{8.17}{278}{\textcolor {Chapter }{A permutation character of the Baby Monster (June{\nobreakspace }2012)}}{section.8.17}{}}
\citation{GMS89}
\@writefile{toc}{\contentsline {section}{\numberline {8.18}\textcolor {Chapter }{A permutation character of $2.B$ (October{\nobreakspace  }2017)}}{280}{section.8.18}\protected@file@percent }
\newlabel{sect:comp_2B}{{8.18}{280}{\textcolor {Chapter }{A permutation character of $2.B$ (October{\nobreakspace }2017)}}{section.8.18}{}}
\@writefile{brf}{\backcite{GMS89}{{280}{8.18}{section.8.18}}}
\citation{BG21}
\citation{BG21}
\citation{Wil98}
\@writefile{toc}{\contentsline {section}{\numberline {8.19}\textcolor {Chapter }{Generation of sporadic simple groups by $\pi $- and $\pi '$-subgroups (December{\nobreakspace  }2021)}}{283}{section.8.19}\protected@file@percent }
\newlabel{sect:comp_pi_piprime}{{8.19}{283}{\textcolor {Chapter }{Generation of sporadic simple groups by $\pi $- and $\pi '$-subgroups (December{\nobreakspace }2021)}}{section.8.19}{}}
\@writefile{brf}{\backcite{BG21}{{283}{8.19}{section.8.19}}}
\@writefile{brf}{\backcite{BG21}{{283}{8.19}{section.8.19}}}
\@writefile{brf}{\backcite{Wil98}{{283}{8.19}{section.8.19}}}
\citation{BG21}
\@writefile{brf}{\backcite{BG21}{{285}{8.19}{section.8.19}}}
\citation{BG21}
\@writefile{brf}{\backcite{BG21}{{287}{8.19}{section.8.19}}}
\citation{AGRv3}
\@writefile{brf}{\backcite{AGRv3}{{288}{8.19}{section.8.19}}}
\citation{NW12}
\citation{Mmaxes}
\@writefile{brf}{\backcite{NW12}{{291}{8.19}{section.8.19}}}
\@writefile{brf}{\backcite{Mmaxes}{{291}{8.19}{section.8.19}}}
\citation{GAP}
\citation{CTblLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {9}\textcolor {Chapter }{Ambiguous Class Fusions in the \textsf  {GAP} Character Table Library}}{293}{chapter.9}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:ambigfus}{{9}{293}{\textcolor {Chapter }{Ambiguous Class Fusions in the \textsf {GAP} Character Table Library}}{chapter.9}{}}
\@writefile{brf}{\backcite{GAP}{{293}{9}{chapter.9}}}
\@writefile{brf}{\backcite{CTblLib}{{293}{9}{chapter.9}}}
\@writefile{toc}{\contentsline {section}{\numberline {9.1}\textcolor {Chapter }{Some \textsf  {GAP} Utilities}}{293}{section.9.1}\protected@file@percent }
\newlabel{sect:GAP_Utilities}{{9.1}{293}{\textcolor {Chapter }{Some \textsf {GAP} Utilities}}{section.9.1}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {9.2}\textcolor {Chapter }{Fusions Determined by Factorization through Intermediate Subgroups}}{294}{section.9.2}\protected@file@percent }
\newlabel{sect:Fusions_Determined_by_Intermediate_Subgroups}{{9.2}{294}{\textcolor {Chapter }{Fusions Determined by Factorization through Intermediate Subgroups}}{section.9.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.1}\textcolor {Chapter }{$Co_3N5 \rightarrow Co_3$ (September 2002)}}{294}{subsection.9.2.1}\protected@file@percent }
\newlabel{subsect:Co_3N5_in_Co_3}{{9.2.1}{294}{\textcolor {Chapter }{$Co_3N5 \rightarrow Co_3$ (September 2002)}}{subsection.9.2.1}{}}
\@writefile{brf}{\backcite{CCN85}{{294}{9.2.1}{subsection.9.2.1}}}
\@writefile{brf}{\backcite{CCN85}{{294}{9.2.1}{subsection.9.2.1}}}
\@writefile{brf}{\backcite{CCN85}{{294}{9.2.1}{subsection.9.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.2}\textcolor {Chapter }{$31:15 \rightarrow B$ (March 2003)}}{295}{subsection.9.2.2}\protected@file@percent }
\newlabel{subsect:31:15_in_B}{{9.2.2}{295}{\textcolor {Chapter }{$31:15 \rightarrow B$ (March 2003)}}{subsection.9.2.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.3}\textcolor {Chapter }{$SuzN3 \rightarrow Suz$ (September 2002)}}{296}{subsection.9.2.3}\protected@file@percent }
\newlabel{subsect:SuzN3_in_Suz}{{9.2.3}{296}{\textcolor {Chapter }{$SuzN3 \rightarrow Suz$ (September 2002)}}{subsection.9.2.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.4}\textcolor {Chapter }{$F_{{3+}}N5 \rightarrow F_{{3+}}$ (March 2002)}}{297}{subsection.9.2.4}\protected@file@percent }
\newlabel{subsect:F3+N5_in_F3+}{{9.2.4}{297}{\textcolor {Chapter }{$F_{{3+}}N5 \rightarrow F_{{3+}}$ (March 2002)}}{subsection.9.2.4}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {9.3}\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Smaller Subgroups}}{298}{section.9.3}\protected@file@percent }
\newlabel{sect:Fusions_Determined_Using_Commutative_Diagrams}{{9.3}{298}{\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Smaller Subgroups}}{section.9.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.1}\textcolor {Chapter }{$BN7 \rightarrow B$ (March 2002)}}{298}{subsection.9.3.1}\protected@file@percent }
\newlabel{subsect:BN7}{{9.3.1}{298}{\textcolor {Chapter }{$BN7 \rightarrow B$ (March 2002)}}{subsection.9.3.1}{}}
\@writefile{brf}{\backcite{CCN85}{{298}{9.3.1}{subsection.9.3.1}}}
\@writefile{brf}{\backcite{CCN85}{{298}{9.3.1}{subsection.9.3.1}}}
\@writefile{brf}{\backcite{CCN85}{{298}{9.3.1}{subsection.9.3.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.2}\textcolor {Chapter }{$(A_4 \times O_8^+(2).3).2 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{299}{subsection.9.3.2}\protected@file@percent }
\newlabel{subsect:A4xO8p2d32fusf3p}{{9.3.2}{299}{\textcolor {Chapter }{$(A_4 \times O_8^+(2).3).2 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{subsection.9.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.3}\textcolor {Chapter }{$A_6 \times L_2(8).3 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{300}{subsection.9.3.3}\protected@file@percent }
\newlabel{subsect:A_6xL_2(8).3_in_Fi24}{{9.3.3}{300}{\textcolor {Chapter }{$A_6 \times L_2(8).3 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{subsection.9.3.3}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.4}\textcolor {Chapter }{$(3^2:D_8 \times U_4(3).2^2).2 \rightarrow B$ (June 2007)}}{301}{subsection.9.3.4}\protected@file@percent }
\newlabel{subsect:BM14}{{9.3.4}{301}{\textcolor {Chapter }{$(3^2:D_8 \times U_4(3).2^2).2 \rightarrow B$ (June 2007)}}{subsection.9.3.4}{}}
\@writefile{brf}{\backcite{CCN85}{{301}{9.3.4}{subsection.9.3.4}}}
\@writefile{brf}{\backcite{CCN85}{{301}{9.3.4}{subsection.9.3.4}}}
\@writefile{brf}{\backcite{CCN85}{{301}{9.3.4}{subsection.9.3.4}}}
\citation{AGRv3}
\citation{AtlasRep}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.5}\textcolor {Chapter }{$7^{1+4}:(3 \times 2.S_7) \rightarrow M$ (May 2009)}}{303}{subsection.9.3.5}\protected@file@percent }
\newlabel{subsect:MM24}{{9.3.5}{303}{\textcolor {Chapter }{$7^{1+4}:(3 \times 2.S_7) \rightarrow M$ (May 2009)}}{subsection.9.3.5}{}}
\@writefile{brf}{\backcite{AGRv3}{{303}{9.3.5}{subsection.9.3.5}}}
\@writefile{brf}{\backcite{AtlasRep}{{303}{9.3.5}{subsection.9.3.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.6}\textcolor {Chapter }{$3^7.O_7(3):2 \rightarrow Fi_{24}$ (November 2010)}}{304}{subsection.9.3.6}\protected@file@percent }
\newlabel{subsect:3^7.O_7(3):2_in_Fi24}{{9.3.6}{304}{\textcolor {Chapter }{$3^7.O_7(3):2 \rightarrow Fi_{24}$ (November 2010)}}{subsection.9.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.3.7}\textcolor {Chapter }{${}^2E_6(2)N3C \rightarrow {}^2E_6(2)$ (January 2019)}}{306}{subsection.9.3.7}\protected@file@percent }
\newlabel{subsect:2E62N3C_in_2E62}{{9.3.7}{306}{\textcolor {Chapter }{${}^2E_6(2)N3C \rightarrow {}^2E_6(2)$ (January 2019)}}{subsection.9.3.7}{}}
\citation{AtlasImpII}
\citation{CCN85}
\@writefile{brf}{\backcite{AtlasImpII}{{309}{9.3.7}{subsection.9.3.7}}}
\@writefile{brf}{\backcite{CCN85}{{309}{9.3.7}{subsection.9.3.7}}}
\@writefile{toc}{\contentsline {section}{\numberline {9.4}\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Factor Groups}}{309}{section.9.4}\protected@file@percent }
\newlabel{sect:Fusions_Determined_Using_Factor_Groups}{{9.4}{309}{\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Factor Groups}}{section.9.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.1}\textcolor {Chapter }{$3.A_7 \rightarrow 3.Suz$ (December 2010)}}{309}{subsection.9.4.1}\protected@file@percent }
\newlabel{subsect:3.A_7_in_3.Suz}{{9.4.1}{309}{\textcolor {Chapter }{$3.A_7 \rightarrow 3.Suz$ (December 2010)}}{subsection.9.4.1}{}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{310}{9.4.1}{subsection.9.4.1}}}
\@writefile{brf}{\backcite{CCN85}{{310}{9.4.1}{subsection.9.4.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.2}\textcolor {Chapter }{$S_6 \rightarrow U_4(2)$ (September 2011)}}{310}{subsection.9.4.2}\protected@file@percent }
\newlabel{subsect:S6_in_U4(2)}{{9.4.2}{310}{\textcolor {Chapter }{$S_6 \rightarrow U_4(2)$ (September 2011)}}{subsection.9.4.2}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {section}{\numberline {9.5}\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Automorphic Extensions}}{311}{section.9.5}\protected@file@percent }
\newlabel{sect:Fusions Determined Using Commutative Diagrams Involving Automorphic Extensions}{{9.5}{311}{\textcolor {Chapter }{Fusions Determined Using Commutative Diagrams Involving Automorphic Extensions}}{section.9.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.5.1}\textcolor {Chapter }{$U_3(8).3_1 \rightarrow {}^2E_6(2)$ (December 2010)}}{311}{subsection.9.5.1}\protected@file@percent }
\newlabel{subsect:u383to2e62}{{9.5.1}{311}{\textcolor {Chapter }{$U_3(8).3_1 \rightarrow {}^2E_6(2)$ (December 2010)}}{subsection.9.5.1}{}}
\@writefile{brf}{\backcite{CCN85}{{311}{9.5.1}{subsection.9.5.1}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{312}{9.5.1}{subsection.9.5.1}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.5.2}\textcolor {Chapter }{$L_3(4).2_1 \rightarrow U_6(2)$ (December 2010)}}{313}{subsection.9.5.2}\protected@file@percent }
\newlabel{subsect:L3421-in-U62}{{9.5.2}{313}{\textcolor {Chapter }{$L_3(4).2_1 \rightarrow U_6(2)$ (December 2010)}}{subsection.9.5.2}{}}
\@writefile{brf}{\backcite{CCN85}{{313}{9.5.2}{subsection.9.5.2}}}
\@writefile{brf}{\backcite{CCN85}{{313}{9.5.2}{subsection.9.5.2}}}
\@writefile{toc}{\contentsline {section}{\numberline {9.6}\textcolor {Chapter }{Conditions Imposed by Brauer Tables}}{315}{section.9.6}\protected@file@percent }
\newlabel{sect:Conditions Imposed by Brauer Tables}{{9.6}{315}{\textcolor {Chapter }{Conditions Imposed by Brauer Tables}}{section.9.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.6.1}\textcolor {Chapter }{$L_2(16).4 \rightarrow J_3.2$ (January{\nobreakspace  }2004)}}{315}{subsection.9.6.1}\protected@file@percent }
\newlabel{subsect:L2(16).4_in_J3.2}{{9.6.1}{315}{\textcolor {Chapter }{$L_2(16).4 \rightarrow J_3.2$ (January{\nobreakspace }2004)}}{subsection.9.6.1}{}}
\citation{CTblLib}
\@writefile{brf}{\backcite{CTblLib}{{316}{9.6.1}{subsection.9.6.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.6.2}\textcolor {Chapter }{$L_2(17) \rightarrow S_8(2)$ (July 2004)}}{316}{subsection.9.6.2}\protected@file@percent }
\newlabel{subsect:L2(17)_in_S8(2)}{{9.6.2}{316}{\textcolor {Chapter }{$L_2(17) \rightarrow S_8(2)$ (July 2004)}}{subsection.9.6.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.6.3}\textcolor {Chapter }{$L_2(19) \rightarrow J_3$ (April 2003)}}{317}{subsection.9.6.3}\protected@file@percent }
\newlabel{subsect:generality}{{9.6.3}{317}{\textcolor {Chapter }{$L_2(19) \rightarrow J_3$ (April 2003)}}{subsection.9.6.3}{}}
\citation{AGRv3}
\citation{AtlasRep}
\@writefile{brf}{\backcite{AGRv3}{{318}{9.6.3}{subsection.9.6.3}}}
\@writefile{brf}{\backcite{AtlasRep}{{318}{9.6.3}{subsection.9.6.3}}}
\citation{AGRv3}
\citation{AtlasRep}
\citation{BN95}
\@writefile{toc}{\contentsline {section}{\numberline {9.7}\textcolor {Chapter }{Fusions Determined by Information about the Groups}}{319}{section.9.7}\protected@file@percent }
\newlabel{sect:Fusions Determined by Information about the Groups}{{9.7}{319}{\textcolor {Chapter }{Fusions Determined by Information about the Groups}}{section.9.7}{}}
\@writefile{brf}{\backcite{AGRv3}{{319}{9.7}{section.9.7}}}
\@writefile{brf}{\backcite{AtlasRep}{{319}{9.7}{section.9.7}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.1}\textcolor {Chapter }{$U_3(3).2 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{320}{subsection.9.7.1}\protected@file@percent }
\newlabel{subsect:U3(3).2_in_Fi24'}{{9.7.1}{320}{\textcolor {Chapter }{$U_3(3).2 \rightarrow Fi_{24}^{\prime }$ (November 2002)}}{subsection.9.7.1}{}}
\@writefile{brf}{\backcite{BN95}{{320}{9.7.1}{subsection.9.7.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.2}\textcolor {Chapter }{$L_2(13).2 \rightarrow Fi_{24}^{\prime }$ (September 2002)}}{321}{subsection.9.7.2}\protected@file@percent }
\newlabel{subsect:L2(13).2_in_Fi24'}{{9.7.2}{321}{\textcolor {Chapter }{$L_2(13).2 \rightarrow Fi_{24}^{\prime }$ (September 2002)}}{subsection.9.7.2}{}}
\citation{LW91}
\@writefile{brf}{\backcite{LW91}{{322}{9.7.2}{subsection.9.7.2}}}
\citation{Wil93a}
\citation{Wil99}
\citation{Wil99}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.3}\textcolor {Chapter }{$M_{11} \rightarrow B$ (April 2009)}}{323}{subsection.9.7.3}\protected@file@percent }
\newlabel{subsect:M11fusB}{{9.7.3}{323}{\textcolor {Chapter }{$M_{11} \rightarrow B$ (April 2009)}}{subsection.9.7.3}{}}
\@writefile{brf}{\backcite{Wil93a}{{323}{9.7.3}{subsection.9.7.3}}}
\@writefile{brf}{\backcite{Wil99}{{323}{9.7.3}{subsection.9.7.3}}}
\@writefile{brf}{\backcite{Wil99}{{323}{9.7.3}{subsection.9.7.3}}}
\citation{Wil93a}
\citation{Wil99}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.4}\textcolor {Chapter }{$L_2(11):2 \rightarrow B$ (April 2009)}}{324}{subsection.9.7.4}\protected@file@percent }
\newlabel{subsect:L2(11):2_in_B}{{9.7.4}{324}{\textcolor {Chapter }{$L_2(11):2 \rightarrow B$ (April 2009)}}{subsection.9.7.4}{}}
\@writefile{brf}{\backcite{Wil93a}{{324}{9.7.4}{subsection.9.7.4}}}
\@writefile{brf}{\backcite{Wil99}{{324}{9.7.4}{subsection.9.7.4}}}
\citation{Wil99}
\citation{Wil99}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.5}\textcolor {Chapter }{$L_3(3) \rightarrow B$ (April 2009)}}{325}{subsection.9.7.5}\protected@file@percent }
\newlabel{subsect:L3(3)_in_B}{{9.7.5}{325}{\textcolor {Chapter }{$L_3(3) \rightarrow B$ (April 2009)}}{subsection.9.7.5}{}}
\@writefile{brf}{\backcite{Wil99}{{325}{9.7.5}{subsection.9.7.5}}}
\@writefile{brf}{\backcite{Wil99}{{325}{9.7.5}{subsection.9.7.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.6}\textcolor {Chapter }{$L_2(17).2 \rightarrow B$ (March 2004)}}{325}{subsection.9.7.6}\protected@file@percent }
\newlabel{subsect:L2(17).2_in_B}{{9.7.6}{325}{\textcolor {Chapter }{$L_2(17).2 \rightarrow B$ (March 2004)}}{subsection.9.7.6}{}}
\citation{Wil99}
\citation{Wilson93}
\citation{Wilson93}
\@writefile{brf}{\backcite{Wil99}{{326}{9.7.6}{subsection.9.7.6}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.7}\textcolor {Chapter }{$L_2(49).2_3 \rightarrow B$ (June 2006)}}{326}{subsection.9.7.7}\protected@file@percent }
\newlabel{subsect:L2(49).2_3_in_B}{{9.7.7}{326}{\textcolor {Chapter }{$L_2(49).2_3 \rightarrow B$ (June 2006)}}{subsection.9.7.7}{}}
\@writefile{brf}{\backcite{Wilson93}{{326}{9.7.7}{subsection.9.7.7}}}
\@writefile{brf}{\backcite{Wilson93}{{326}{9.7.7}{subsection.9.7.7}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.8}\textcolor {Chapter }{$2^3.L_3(2) \rightarrow G_2(5)$ (January{\nobreakspace  }2004)}}{328}{subsection.9.7.8}\protected@file@percent }
\newlabel{subsect:2^3.L3(2)_in_G2(5)}{{9.7.8}{328}{\textcolor {Chapter }{$2^3.L_3(2) \rightarrow G_2(5)$ (January{\nobreakspace }2004)}}{subsection.9.7.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.9}\textcolor {Chapter }{$5^{{1+4}}.2^{{1+4}}.A_5.4 \rightarrow B$ (April 2009)}}{329}{subsection.9.7.9}\protected@file@percent }
\newlabel{subsect:5^{1+4}.2^{1+4}.A_5.4_in_B}{{9.7.9}{329}{\textcolor {Chapter }{$5^{{1+4}}.2^{{1+4}}.A_5.4 \rightarrow B$ (April 2009)}}{subsection.9.7.9}{}}
\citation{AGRv3}
\citation{AtlasRep}
\@writefile{brf}{\backcite{AGRv3}{{330}{9.7.9}{subsection.9.7.9}}}
\@writefile{brf}{\backcite{AtlasRep}{{330}{9.7.9}{subsection.9.7.9}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.10}\textcolor {Chapter }{The fusion from the character table of $7^2:2L_2(7).2$ into the table of marks (January{\nobreakspace  }2004)}}{330}{subsection.9.7.10}\protected@file@percent }
\newlabel{subsect:7^2:2L_2(7).2_tom}{{9.7.10}{330}{\textcolor {Chapter }{The fusion from the character table of $7^2:2L_2(7).2$ into the table of marks (January{\nobreakspace }2004)}}{subsection.9.7.10}{}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.11}\textcolor {Chapter }{$3 \times U_4(2) \rightarrow 3_1.U_4(3)$ (March 2010)}}{333}{subsection.9.7.11}\protected@file@percent }
\newlabel{subsect:3xU_4(2)_in_3_1.U_4(3)}{{9.7.11}{333}{\textcolor {Chapter }{$3 \times U_4(2) \rightarrow 3_1.U_4(3)$ (March 2010)}}{subsection.9.7.11}{}}
\@writefile{brf}{\backcite{CCN85}{{333}{9.7.11}{subsection.9.7.11}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.12}\textcolor {Chapter }{$2.3^4.2^3.S_4 \rightarrow 2.A12$ (September 2011)}}{335}{subsection.9.7.12}\protected@file@percent }
\newlabel{subsect:2.3^4.2^3.S_4_in_2.A12}{{9.7.12}{335}{\textcolor {Chapter }{$2.3^4.2^3.S_4 \rightarrow 2.A12$ (September 2011)}}{subsection.9.7.12}{}}
\citation{AGRv3}
\@writefile{brf}{\backcite{AGRv3}{{336}{9.7.12}{subsection.9.7.12}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.13}\textcolor {Chapter }{$127:7 \rightarrow L_7(2)$ (January 2012)}}{337}{subsection.9.7.13}\protected@file@percent }
\newlabel{subsect:127:7_in_L_7(2)}{{9.7.13}{337}{\textcolor {Chapter }{$127:7 \rightarrow L_7(2)$ (January 2012)}}{subsection.9.7.13}{}}
\citation{HW04}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.14}\textcolor {Chapter }{$L_2(59) \rightarrow M$ (May 2009)}}{338}{subsection.9.7.14}\protected@file@percent }
\newlabel{subsect:L_2(59)_in_M}{{9.7.14}{338}{\textcolor {Chapter }{$L_2(59) \rightarrow M$ (May 2009)}}{subsection.9.7.14}{}}
\@writefile{brf}{\backcite{HW04}{{338}{9.7.14}{subsection.9.7.14}}}
\citation{HW04}
\citation{HW08}
\@writefile{brf}{\backcite{HW04}{{339}{9.7.14}{subsection.9.7.14}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.15}\textcolor {Chapter }{$L_2(71) \rightarrow M$ (May 2009)}}{339}{subsection.9.7.15}\protected@file@percent }
\newlabel{subsect:L2(71)_in_M}{{9.7.15}{339}{\textcolor {Chapter }{$L_2(71) \rightarrow M$ (May 2009)}}{subsection.9.7.15}{}}
\@writefile{brf}{\backcite{HW08}{{339}{9.7.15}{subsection.9.7.15}}}
\citation{NW02}
\citation{NW12}
\@writefile{brf}{\backcite{NW02}{{340}{9.7.15}{subsection.9.7.15}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.7.16}\textcolor {Chapter }{$L_2(41) \rightarrow M$ (April 2012)}}{340}{subsection.9.7.16}\protected@file@percent }
\newlabel{subsect:L_2(41)_in_M}{{9.7.16}{340}{\textcolor {Chapter }{$L_2(41) \rightarrow M$ (April 2012)}}{subsection.9.7.16}{}}
\@writefile{brf}{\backcite{NW12}{{340}{9.7.16}{subsection.9.7.16}}}
\citation{NW12}
\@writefile{brf}{\backcite{NW12}{{341}{9.7.16}{subsection.9.7.16}}}
\citation{DNT}
\citation{DNT}
\citation{JLPW95}
\citation{AGRv3}
\citation{GAP}
\citation{AtlasRep}
\citation{cohomolo}
\citation{CTblLib}
\citation{TomLib}
\@writefile{toc}{\contentsline {chapter}{\numberline {10}\textcolor {Chapter }{\textsf  {GAP} computations needed in the proof of \cite  [Theorem 6.1 (ii)]{DNT}}}{342}{chapter.10}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{brf}{\backcite{DNT}{{342}{10}{chapter.10}}}
\newlabel{chap:dntgap}{{10}{342}{\textcolor {Chapter }{\textsf {GAP} computations needed in the proof of \cite [Theorem 6.1 (ii)]{DNT}}}{chapter.10}{}}
\@writefile{brf}{\backcite{DNT}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{JLPW95}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{AGRv3}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{GAP}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{AtlasRep}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{cohomolo}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{CTblLib}{{342}{10}{chapter.10}}}
\@writefile{brf}{\backcite{TomLib}{{342}{10}{chapter.10}}}
\@writefile{toc}{\contentsline {section}{\numberline {10.1}\textcolor {Chapter }{$G/N \cong  Sz(8)$ and $|N| = 2^{12}$}}{342}{section.10.1}\protected@file@percent }
\newlabel{sect:Sz8,2^12}{{10.1}{342}{\textcolor {Chapter }{$G/N \cong Sz(8)$ and $|N| = 2^{12}$}}{section.10.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.2}\textcolor {Chapter }{$G/N \cong  M_{22}$ and $|N| = 2^{10}$}}{344}{section.10.2}\protected@file@percent }
\newlabel{sect:M22,2^10}{{10.2}{344}{\textcolor {Chapter }{$G/N \cong M_{22}$ and $|N| = 2^{10}$}}{section.10.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.3}\textcolor {Chapter }{$G/N \cong  J_2$ and $|N| = 2^{12}$}}{347}{section.10.3}\protected@file@percent }
\newlabel{sect:J2,2^12}{{10.3}{347}{\textcolor {Chapter }{$G/N \cong J_2$ and $|N| = 2^{12}$}}{section.10.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.4}\textcolor {Chapter }{$G/N \cong  J_2$ and $|N| = 5^{14}$}}{348}{section.10.4}\protected@file@percent }
\newlabel{sect:J2,5^14}{{10.4}{348}{\textcolor {Chapter }{$G/N \cong J_2$ and $|N| = 5^{14}$}}{section.10.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.5}\textcolor {Chapter }{$G/N \cong  J_2$ and $|N| = 2^{28}$}}{351}{section.10.5}\protected@file@percent }
\newlabel{sect:J2,2^28}{{10.5}{351}{\textcolor {Chapter }{$G/N \cong J_2$ and $|N| = 2^{28}$}}{section.10.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.6}\textcolor {Chapter }{$G/N \cong  {}^3D_4(2)$ and $|N| = 2^{26}$}}{352}{section.10.6}\protected@file@percent }
\newlabel{sect:cong}{{10.6}{352}{\textcolor {Chapter }{$G/N \cong {}^3D_4(2)$ and $|N| = 2^{26}$}}{section.10.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10.7}\textcolor {Chapter }{$G/N \cong  {}^3D_4(2)$ and $|N| = 3^{25}$}}{355}{section.10.7}\protected@file@percent }
\newlabel{sect:}{{10.7}{355}{\textcolor {Chapter }{$G/N \cong {}^3D_4(2)$ and $|N| = 3^{25}$}}{section.10.7}{}}
\citation{GAP}
\citation{BGK}
\citation{BGK}
\@writefile{toc}{\contentsline {chapter}{\numberline {11}\textcolor {Chapter }{\textsf  {GAP} Computations Concerning Probabilistic Generation of Finite Simple Groups}}{356}{chapter.11}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:probgen}{{11}{356}{\textcolor {Chapter }{\textsf {GAP} Computations Concerning Probabilistic Generation of Finite Simple Groups}}{chapter.11}{}}
\@writefile{brf}{\backcite{GAP}{{356}{11}{chapter.11}}}
\@writefile{brf}{\backcite{BGK}{{356}{11}{chapter.11}}}
\@writefile{toc}{\contentsline {section}{\numberline {11.1}\textcolor {Chapter }{Overview}}{356}{section.11.1}\protected@file@percent }
\newlabel{sect:probgen_overview}{{11.1}{356}{\textcolor {Chapter }{Overview}}{section.11.1}{}}
\@writefile{brf}{\backcite{BGK}{{356}{11.1}{section.11.1}}}
\citation{CTblLib}
\@writefile{brf}{\backcite{CTblLib}{{357}{11.1}{section.11.1}}}
\citation{BGK}
\citation{BGK}
\citation{CCN85}
\citation{BGK}
\citation{AtlasRep}
\citation{AGRv3}
\@writefile{brf}{\backcite{BGK}{{359}{11.1}{section.11.1}}}
\@writefile{brf}{\backcite{BGK}{{359}{11.1}{section.11.1}}}
\@writefile{brf}{\backcite{CCN85}{{359}{11.1}{section.11.1}}}
\@writefile{brf}{\backcite{BGK}{{359}{11.1}{section.11.1}}}
\@writefile{brf}{\backcite{AtlasRep}{{359}{11.1}{section.11.1}}}
\@writefile{brf}{\backcite{AGRv3}{{359}{11.1}{section.11.1}}}
\@writefile{toc}{\contentsline {section}{\numberline {11.2}\textcolor {Chapter }{Prerequisites}}{360}{section.11.2}\protected@file@percent }
\newlabel{sect:probgen-background}{{11.2}{360}{\textcolor {Chapter }{Prerequisites}}{section.11.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.1}\textcolor {Chapter }{Theoretical Background}}{360}{subsection.11.2.1}\protected@file@percent }
\newlabel{sect:Theoretical Background}{{11.2.1}{360}{\textcolor {Chapter }{Theoretical Background}}{subsection.11.2.1}{}}
\citation{BGK}
\citation{GK}
\citation{BGK}
\citation{BGK}
\@writefile{brf}{\backcite{BGK}{{361}{11.2.1}{subsection.11.2.1}}}
\@writefile{brf}{\backcite{GK}{{361}{11.2.1}{subsection.11.2.1}}}
\@writefile{brf}{\backcite{BGK}{{361}{11.2.1}{subsection.11.2.1}}}
\@writefile{brf}{\backcite{BGK}{{361}{11.2.1}{subsection.11.2.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.2.2}\textcolor {Chapter }{Computational Criteria}}{361}{subsection.11.2.2}\protected@file@percent }
\newlabel{sect:probgen-criteria}{{11.2.2}{361}{\textcolor {Chapter }{Computational Criteria}}{subsection.11.2.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {11.3}\textcolor {Chapter }{\textsf  {GAP} Functions for the Computations}}{362}{section.11.3}\protected@file@percent }
\newlabel{sect:probgen-functions}{{11.3}{362}{\textcolor {Chapter }{\textsf {GAP} Functions for the Computations}}{section.11.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.1}\textcolor {Chapter }{General Utilities}}{362}{subsection.11.3.1}\protected@file@percent }
\newlabel{subsect:utils}{{11.3.1}{362}{\textcolor {Chapter }{General Utilities}}{subsection.11.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.2}\textcolor {Chapter }{Character-Theoretic Computations}}{364}{subsection.11.3.2}\protected@file@percent }
\newlabel{subsect:probgen-ctfun}{{11.3.2}{364}{\textcolor {Chapter }{Character-Theoretic Computations}}{subsection.11.3.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.3.3}\textcolor {Chapter }{Computations with Groups}}{369}{subsection.11.3.3}\protected@file@percent }
\newlabel{subsect:groups}{{11.3.3}{369}{\textcolor {Chapter }{Computations with Groups}}{subsection.11.3.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {11.4}\textcolor {Chapter }{Character-Theoretic Computations}}{377}{section.11.4}\protected@file@percent }
\newlabel{sect:chartheor}{{11.4}{377}{\textcolor {Chapter }{Character-Theoretic Computations}}{section.11.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.1}\textcolor {Chapter }{Sporadic Simple Groups}}{377}{subsection.11.4.1}\protected@file@percent }
\newlabel{subsect:spor}{{11.4.1}{377}{\textcolor {Chapter }{Sporadic Simple Groups}}{subsection.11.4.1}{}}
\citation{Wil99}
\citation{HW04}
\citation{GM01}
\citation{GM01}
\@writefile{brf}{\backcite{Wil99}{{379}{11.4.1}{subsection.11.4.1}}}
\@writefile{brf}{\backcite{HW04}{{379}{11.4.1}{subsection.11.4.1}}}
\@writefile{brf}{\backcite{GM01}{{379}{11.4.1}{subsection.11.4.1}}}
\@writefile{brf}{\backcite{GM01}{{379}{11.4.1}{subsection.11.4.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.2}\textcolor {Chapter }{Automorphism Groups of Sporadic Simple Groups}}{379}{subsection.11.4.2}\protected@file@percent }
\newlabel{probgen:sporaut}{{11.4.2}{379}{\textcolor {Chapter }{Automorphism Groups of Sporadic Simple Groups}}{subsection.11.4.2}{}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{382}{11.4.2}{subsection.11.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{382}{11.4.2}{subsection.11.4.2}}}
\citation{CCN85}
\citation{CCN85}
\citation{BGK}
\@writefile{brf}{\backcite{CCN85}{{383}{11.4.2}{subsection.11.4.2}}}
\@writefile{brf}{\backcite{CCN85}{{383}{11.4.2}{subsection.11.4.2}}}
\@writefile{brf}{\backcite{BGK}{{384}{11.4.2}{subsection.11.4.2}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{385}{11.4.2}{subsection.11.4.2}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{386}{11.4.2}{subsection.11.4.2}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.3}\textcolor {Chapter }{Other Simple Groups {\textendash } Easy Cases}}{386}{subsection.11.4.3}\protected@file@percent }
\newlabel{easyloop}{{11.4.3}{386}{\textcolor {Chapter }{Other Simple Groups {\textendash } Easy Cases}}{subsection.11.4.3}{}}
\citation{BGK}
\citation{BGK}
\@writefile{brf}{\backcite{BGK}{{387}{11.4.3}{subsection.11.4.3}}}
\@writefile{brf}{\backcite{BGK}{{387}{11.4.3}{subsection.11.4.3}}}
\citation{BW1}
\citation{BW1}
\citation{BGK}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{BW1}{{389}{11.4.3}{subsection.11.4.3}}}
\@writefile{brf}{\backcite{BW1}{{389}{11.4.3}{subsection.11.4.3}}}
\@writefile{brf}{\backcite{BGK}{{389}{11.4.3}{subsection.11.4.3}}}
\@writefile{brf}{\backcite{CCN85}{{389}{11.4.3}{subsection.11.4.3}}}
\@writefile{brf}{\backcite{CCN85}{{389}{11.4.3}{subsection.11.4.3}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.4}\textcolor {Chapter }{Automorphism Groups of other Simple Groups {\textendash } Easy Cases}}{390}{subsection.11.4.4}\protected@file@percent }
\newlabel{easyloopaut}{{11.4.4}{390}{\textcolor {Chapter }{Automorphism Groups of other Simple Groups {\textendash } Easy Cases}}{subsection.11.4.4}{}}
\citation{BGK}
\citation{CCN85}
\@writefile{brf}{\backcite{BGK}{{391}{11.4.4}{subsection.11.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{391}{11.4.4}{subsection.11.4.4}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{392}{11.4.4}{subsection.11.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{392}{11.4.4}{subsection.11.4.4}}}
\@writefile{brf}{\backcite{CCN85}{{392}{11.4.4}{subsection.11.4.4}}}
\citation{CCN85}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.5}\textcolor {Chapter }{$O_8^-(3)$}}{393}{subsection.11.4.5}\protected@file@percent }
\newlabel{O8m3}{{11.4.5}{393}{\textcolor {Chapter }{$O_8^-(3)$}}{subsection.11.4.5}{}}
\@writefile{brf}{\backcite{CCN85}{{393}{11.4.5}{subsection.11.4.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.6}\textcolor {Chapter }{$O_{10}^+(2)$}}{393}{subsection.11.4.6}\protected@file@percent }
\newlabel{O10p2}{{11.4.6}{393}{\textcolor {Chapter }{$O_{10}^+(2)$}}{subsection.11.4.6}{}}
\@writefile{brf}{\backcite{CCN85}{{393}{11.4.6}{subsection.11.4.6}}}
\citation{CCN85}
\citation{CCN85}
\citation{Auto}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.7}\textcolor {Chapter }{$O_{10}^-(2)$}}{394}{subsection.11.4.7}\protected@file@percent }
\newlabel{O10m2}{{11.4.7}{394}{\textcolor {Chapter }{$O_{10}^-(2)$}}{subsection.11.4.7}{}}
\@writefile{brf}{\backcite{CCN85}{{394}{11.4.7}{subsection.11.4.7}}}
\@writefile{brf}{\backcite{CCN85}{{394}{11.4.7}{subsection.11.4.7}}}
\@writefile{brf}{\backcite{Auto}{{394}{11.4.7}{subsection.11.4.7}}}
\citation{GPPS}
\citation{KlL90}
\citation{KlL90}
\citation{GPPS}
\citation{KlL90}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.8}\textcolor {Chapter }{$O_{12}^+(2)$}}{395}{subsection.11.4.8}\protected@file@percent }
\newlabel{O12p2}{{11.4.8}{395}{\textcolor {Chapter }{$O_{12}^+(2)$}}{subsection.11.4.8}{}}
\@writefile{brf}{\backcite{GPPS}{{395}{11.4.8}{subsection.11.4.8}}}
\@writefile{brf}{\backcite{KlL90}{{395}{11.4.8}{subsection.11.4.8}}}
\@writefile{brf}{\backcite{KlL90}{{395}{11.4.8}{subsection.11.4.8}}}
\@writefile{brf}{\backcite{GPPS}{{395}{11.4.8}{subsection.11.4.8}}}
\@writefile{brf}{\backcite{KlL90}{{395}{11.4.8}{subsection.11.4.8}}}
\citation{BGK}
\citation{Be00}
\citation{KlL90}
\@writefile{brf}{\backcite{BGK}{{397}{11.4.8}{subsection.11.4.8}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.9}\textcolor {Chapter }{$O_{12}^-(2)$}}{397}{subsection.11.4.9}\protected@file@percent }
\newlabel{O12m2}{{11.4.9}{397}{\textcolor {Chapter }{$O_{12}^-(2)$}}{subsection.11.4.9}{}}
\@writefile{brf}{\backcite{Be00}{{397}{11.4.9}{subsection.11.4.9}}}
\@writefile{brf}{\backcite{KlL90}{{397}{11.4.9}{subsection.11.4.9}}}
\citation{Be00}
\citation{KlL90}
\citation{BP98copy}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.10}\textcolor {Chapter }{$S_6(4)$}}{398}{subsection.11.4.10}\protected@file@percent }
\newlabel{S64}{{11.4.10}{398}{\textcolor {Chapter }{$S_6(4)$}}{subsection.11.4.10}{}}
\@writefile{brf}{\backcite{Be00}{{398}{11.4.10}{subsection.11.4.10}}}
\@writefile{brf}{\backcite{KlL90}{{398}{11.4.10}{subsection.11.4.10}}}
\@writefile{brf}{\backcite{BP98copy}{{398}{11.4.10}{subsection.11.4.10}}}
\citation{BGK}
\citation{GPPS}
\citation{GPPS}
\citation{KlL90}
\@writefile{brf}{\backcite{BGK}{{399}{11.4.10}{subsection.11.4.10}}}
\citation{GPPS}
\citation{GPPS}
\citation{KlL90}
\citation{KlL90}
\@writefile{brf}{\backcite{GPPS}{{400}{11.4.10}{subsection.11.4.10}}}
\@writefile{brf}{\backcite{GPPS}{{400}{11.4.10}{subsection.11.4.10}}}
\@writefile{brf}{\backcite{KlL90}{{400}{11.4.10}{subsection.11.4.10}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.11}\textcolor {Chapter }{$\ast ${\nobreakspace  }$S_6(5)$}}{400}{subsection.11.4.11}\protected@file@percent }
\newlabel{S65}{{11.4.11}{400}{\textcolor {Chapter }{$\ast ${\nobreakspace }$S_6(5)$}}{subsection.11.4.11}{}}
\@writefile{brf}{\backcite{GPPS}{{400}{11.4.11}{subsection.11.4.11}}}
\@writefile{brf}{\backcite{GPPS}{{400}{11.4.11}{subsection.11.4.11}}}
\@writefile{brf}{\backcite{KlL90}{{400}{11.4.11}{subsection.11.4.11}}}
\@writefile{brf}{\backcite{KlL90}{{400}{11.4.11}{subsection.11.4.11}}}
\citation{Be00}
\citation{KlL90}
\citation{KlL90}
\citation{MSW94}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.12}\textcolor {Chapter }{$S_8(3)$}}{401}{subsection.11.4.12}\protected@file@percent }
\newlabel{S83}{{11.4.12}{401}{\textcolor {Chapter }{$S_8(3)$}}{subsection.11.4.12}{}}
\@writefile{brf}{\backcite{Be00}{{401}{11.4.12}{subsection.11.4.12}}}
\@writefile{brf}{\backcite{KlL90}{{401}{11.4.12}{subsection.11.4.12}}}
\@writefile{brf}{\backcite{KlL90}{{401}{11.4.12}{subsection.11.4.12}}}
\citation{BP98copy}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.13}\textcolor {Chapter }{$U_4(4)$}}{402}{subsection.11.4.13}\protected@file@percent }
\newlabel{U44}{{11.4.13}{402}{\textcolor {Chapter }{$U_4(4)$}}{subsection.11.4.13}{}}
\@writefile{brf}{\backcite{MSW94}{{402}{11.4.13}{subsection.11.4.13}}}
\@writefile{brf}{\backcite{BP98copy}{{402}{11.4.13}{subsection.11.4.13}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.4.14}\textcolor {Chapter }{$U_6(2)$}}{402}{subsection.11.4.14}\protected@file@percent }
\newlabel{U62}{{11.4.14}{402}{\textcolor {Chapter }{$U_6(2)$}}{subsection.11.4.14}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{403}{11.4.14}{subsection.11.4.14}}}
\@writefile{brf}{\backcite{CCN85}{{403}{11.4.14}{subsection.11.4.14}}}
\citation{CCN85}
\citation{BGK}
\citation{HulpkeTG}
\@writefile{brf}{\backcite{CCN85}{{404}{11.4.14}{subsection.11.4.14}}}
\@writefile{toc}{\contentsline {section}{\numberline {11.5}\textcolor {Chapter }{Computations using Groups}}{404}{section.11.5}\protected@file@percent }
\newlabel{sect:hard}{{11.5}{404}{\textcolor {Chapter }{Computations using Groups}}{section.11.5}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.1}\textcolor {Chapter }{$A_{2m+1}$, $2 \leq m \leq 11$}}{404}{subsection.11.5.1}\protected@file@percent }
\newlabel{Aodd}{{11.5.1}{404}{\textcolor {Chapter }{$A_{2m+1}$, $2 \leq m \leq 11$}}{subsection.11.5.1}{}}
\@writefile{brf}{\backcite{BGK}{{404}{11.5.1}{subsection.11.5.1}}}
\@writefile{brf}{\backcite{HulpkeTG}{{404}{11.5.1}{subsection.11.5.1}}}
\citation{BW1}
\citation{BW1}
\citation{CCN85}
\@writefile{brf}{\backcite{BW1}{{406}{11.5.1}{subsection.11.5.1}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.2}\textcolor {Chapter }{$A_5$}}{406}{subsection.11.5.2}\protected@file@percent }
\newlabel{A5}{{11.5.2}{406}{\textcolor {Chapter }{$A_5$}}{subsection.11.5.2}{}}
\@writefile{brf}{\backcite{BW1}{{406}{11.5.2}{subsection.11.5.2}}}
\@writefile{brf}{\backcite{CCN85}{{406}{11.5.2}{subsection.11.5.2}}}
\citation{BW1}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.3}\textcolor {Chapter }{$A_6$}}{407}{subsection.11.5.3}\protected@file@percent }
\newlabel{A6}{{11.5.3}{407}{\textcolor {Chapter }{$A_6$}}{subsection.11.5.3}{}}
\@writefile{brf}{\backcite{BW1}{{407}{11.5.3}{subsection.11.5.3}}}
\@writefile{brf}{\backcite{CCN85}{{407}{11.5.3}{subsection.11.5.3}}}
\citation{BW1}
\@writefile{brf}{\backcite{BW1}{{408}{11.5.3}{subsection.11.5.3}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.4}\textcolor {Chapter }{$A_7$}}{411}{subsection.11.5.4}\protected@file@percent }
\newlabel{A7}{{11.5.4}{411}{\textcolor {Chapter }{$A_7$}}{subsection.11.5.4}{}}
\@writefile{brf}{\backcite{CCN85}{{411}{11.5.4}{subsection.11.5.4}}}
\citation{BGK}
\citation{Be00}
\citation{BGK}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.5}\textcolor {Chapter }{$L_d(q)$}}{414}{subsection.11.5.5}\protected@file@percent }
\newlabel{SL}{{11.5.5}{414}{\textcolor {Chapter }{$L_d(q)$}}{subsection.11.5.5}{}}
\@writefile{brf}{\backcite{BGK}{{414}{11.5.5}{subsection.11.5.5}}}
\@writefile{brf}{\backcite{Be00}{{414}{11.5.5}{subsection.11.5.5}}}
\@writefile{brf}{\backcite{BGK}{{414}{11.5.5}{subsection.11.5.5}}}
\citation{BGK}
\@writefile{brf}{\backcite{BGK}{{415}{11.5.5}{subsection.11.5.5}}}
\citation{BGK}
\citation{CCN85}
\citation{BGK}
\@writefile{brf}{\backcite{BGK}{{416}{11.5.5}{subsection.11.5.5}}}
\@writefile{brf}{\backcite{CCN85}{{416}{11.5.5}{subsection.11.5.5}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.6}\textcolor {Chapter }{$\ast ${\nobreakspace  }$L_d(q)$ with prime $d$}}{416}{subsection.11.5.6}\protected@file@percent }
\newlabel{subsect:Ldq-with-prime-d}{{11.5.6}{416}{\textcolor {Chapter }{$\ast ${\nobreakspace }$L_d(q)$ with prime $d$}}{subsection.11.5.6}{}}
\@writefile{brf}{\backcite{BGK}{{416}{11.5.6}{subsection.11.5.6}}}
\citation{BGK}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.7}\textcolor {Chapter }{Automorphic Extensions of $L_d(q)$}}{418}{subsection.11.5.7}\protected@file@percent }
\newlabel{SLaut}{{11.5.7}{418}{\textcolor {Chapter }{Automorphic Extensions of $L_d(q)$}}{subsection.11.5.7}{}}
\@writefile{brf}{\backcite{BGK}{{418}{11.5.7}{subsection.11.5.7}}}
\citation{BGK}
\citation{BGK}
\@writefile{brf}{\backcite{BGK}{{422}{11.5.7}{subsection.11.5.7}}}
\@writefile{brf}{\backcite{BGK}{{422}{11.5.7}{subsection.11.5.7}}}
\citation{BW1}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.8}\textcolor {Chapter }{$L_3(2)$}}{425}{subsection.11.5.8}\protected@file@percent }
\newlabel{L32}{{11.5.8}{425}{\textcolor {Chapter }{$L_3(2)$}}{subsection.11.5.8}{}}
\@writefile{brf}{\backcite{BW1}{{425}{11.5.8}{subsection.11.5.8}}}
\@writefile{brf}{\backcite{CCN85}{{425}{11.5.8}{subsection.11.5.8}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.9}\textcolor {Chapter }{$M_{11}$}}{428}{subsection.11.5.9}\protected@file@percent }
\newlabel{spreadM11}{{11.5.9}{428}{\textcolor {Chapter }{$M_{11}$}}{subsection.11.5.9}{}}
\@writefile{brf}{\backcite{CCN85}{{428}{11.5.9}{subsection.11.5.9}}}
\citation{AGRv3}
\@writefile{brf}{\backcite{AGRv3}{{429}{11.5.9}{subsection.11.5.9}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.10}\textcolor {Chapter }{$M_{12}$}}{430}{subsection.11.5.10}\protected@file@percent }
\newlabel{spreadM12}{{11.5.10}{430}{\textcolor {Chapter }{$M_{12}$}}{subsection.11.5.10}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{431}{11.5.10}{subsection.11.5.10}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.11}\textcolor {Chapter }{$O_7(3)$}}{432}{subsection.11.5.11}\protected@file@percent }
\newlabel{O73}{{11.5.11}{432}{\textcolor {Chapter }{$O_7(3)$}}{subsection.11.5.11}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{434}{11.5.11}{subsection.11.5.11}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{437}{11.5.11}{subsection.11.5.11}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.12}\textcolor {Chapter }{$O_8^+(2)$}}{437}{subsection.11.5.12}\protected@file@percent }
\newlabel{O8p2}{{11.5.12}{437}{\textcolor {Chapter }{$O_8^+(2)$}}{subsection.11.5.12}{}}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{438}{11.5.12}{subsection.11.5.12}}}
\@writefile{brf}{\backcite{CCN85}{{438}{11.5.12}{subsection.11.5.12}}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{441}{11.5.12}{subsection.11.5.12}}}
\@writefile{brf}{\backcite{CCN85}{{441}{11.5.12}{subsection.11.5.12}}}
\citation{BGK}
\@writefile{brf}{\backcite{CCN85}{{442}{11.5.12}{subsection.11.5.12}}}
\@writefile{brf}{\backcite{BGK}{{442}{11.5.12}{subsection.11.5.12}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.13}\textcolor {Chapter }{$O_8^+(3)$}}{443}{subsection.11.5.13}\protected@file@percent }
\newlabel{O8p3}{{11.5.13}{443}{\textcolor {Chapter }{$O_8^+(3)$}}{subsection.11.5.13}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{444}{11.5.13}{subsection.11.5.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{451}{11.5.13}{subsection.11.5.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{452}{11.5.13}{subsection.11.5.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{454}{11.5.13}{subsection.11.5.13}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{455}{11.5.13}{subsection.11.5.13}}}
\citation{CCN85}
\citation{Kle87}
\@writefile{brf}{\backcite{CCN85}{{456}{11.5.13}{subsection.11.5.13}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.14}\textcolor {Chapter }{$O^+_8(4)$}}{456}{subsection.11.5.14}\protected@file@percent }
\newlabel{O8p4}{{11.5.14}{456}{\textcolor {Chapter }{$O^+_8(4)$}}{subsection.11.5.14}{}}
\@writefile{brf}{\backcite{Kle87}{{456}{11.5.14}{subsection.11.5.14}}}
\citation{Kle87}
\citation{BGK}
\citation{Kle87}
\citation{BGK}
\citation{MSW94}
\@writefile{brf}{\backcite{Kle87}{{459}{11.5.14}{subsection.11.5.14}}}
\@writefile{brf}{\backcite{BGK}{{459}{11.5.14}{subsection.11.5.14}}}
\@writefile{brf}{\backcite{Kle87}{{459}{11.5.14}{subsection.11.5.14}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.15}\textcolor {Chapter }{$\ast ${\nobreakspace  }$O_9(3)$}}{459}{subsection.11.5.15}\protected@file@percent }
\newlabel{O93}{{11.5.15}{459}{\textcolor {Chapter }{$\ast ${\nobreakspace }$O_9(3)$}}{subsection.11.5.15}{}}
\@writefile{brf}{\backcite{BGK}{{459}{11.5.15}{subsection.11.5.15}}}
\@writefile{brf}{\backcite{MSW94}{{460}{11.5.15}{subsection.11.5.15}}}
\citation{Be00}
\citation{KlL90}
\citation{BGK}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.16}\textcolor {Chapter }{$O_{10}^-(3)$}}{461}{subsection.11.5.16}\protected@file@percent }
\newlabel{O10m3}{{11.5.16}{461}{\textcolor {Chapter }{$O_{10}^-(3)$}}{subsection.11.5.16}{}}
\@writefile{brf}{\backcite{Be00}{{461}{11.5.16}{subsection.11.5.16}}}
\@writefile{brf}{\backcite{KlL90}{{461}{11.5.16}{subsection.11.5.16}}}
\@writefile{brf}{\backcite{BGK}{{461}{11.5.16}{subsection.11.5.16}}}
\citation{Be00}
\citation{KlL90}
\citation{BGK}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.17}\textcolor {Chapter }{$O_{14}^-(2)$}}{463}{subsection.11.5.17}\protected@file@percent }
\newlabel{O14m2}{{11.5.17}{463}{\textcolor {Chapter }{$O_{14}^-(2)$}}{subsection.11.5.17}{}}
\@writefile{brf}{\backcite{Be00}{{463}{11.5.17}{subsection.11.5.17}}}
\@writefile{brf}{\backcite{KlL90}{{463}{11.5.17}{subsection.11.5.17}}}
\@writefile{brf}{\backcite{BGK}{{463}{11.5.17}{subsection.11.5.17}}}
\citation{BGK}
\citation{GK}
\citation{KlL90}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.18}\textcolor {Chapter }{$O_{12}^+(3)$}}{465}{subsection.11.5.18}\protected@file@percent }
\newlabel{O12p3}{{11.5.18}{465}{\textcolor {Chapter }{$O_{12}^+(3)$}}{subsection.11.5.18}{}}
\@writefile{brf}{\backcite{BGK}{{465}{11.5.18}{subsection.11.5.18}}}
\@writefile{brf}{\backcite{GK}{{465}{11.5.18}{subsection.11.5.18}}}
\@writefile{brf}{\backcite{KlL90}{{465}{11.5.18}{subsection.11.5.18}}}
\citation{Be00}
\citation{KlL90}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.19}\textcolor {Chapter }{$\ast ${\nobreakspace  }$S_4(8)$}}{467}{subsection.11.5.19}\protected@file@percent }
\newlabel{S48}{{11.5.19}{467}{\textcolor {Chapter }{$\ast ${\nobreakspace }$S_4(8)$}}{subsection.11.5.19}{}}
\@writefile{brf}{\backcite{Be00}{{467}{11.5.19}{subsection.11.5.19}}}
\@writefile{brf}{\backcite{KlL90}{{467}{11.5.19}{subsection.11.5.19}}}
\citation{CCN85}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.20}\textcolor {Chapter }{$S_6(2)$}}{469}{subsection.11.5.20}\protected@file@percent }
\newlabel{S62}{{11.5.20}{469}{\textcolor {Chapter }{$S_6(2)$}}{subsection.11.5.20}{}}
\@writefile{brf}{\backcite{CCN85}{{470}{11.5.20}{subsection.11.5.20}}}
\citation{CCN85}
\citation{AmbigFus}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.21}\textcolor {Chapter }{$S_8(2)$}}{472}{subsection.11.5.21}\protected@file@percent }
\newlabel{S82}{{11.5.21}{472}{\textcolor {Chapter }{$S_8(2)$}}{subsection.11.5.21}{}}
\@writefile{brf}{\backcite{CCN85}{{472}{11.5.21}{subsection.11.5.21}}}
\@writefile{brf}{\backcite{AmbigFus}{{472}{11.5.21}{subsection.11.5.21}}}
\citation{Be00}
\citation{KlL90}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.22}\textcolor {Chapter }{$\ast ${\nobreakspace  }$S_{10}(2)$}}{473}{subsection.11.5.22}\protected@file@percent }
\newlabel{S102}{{11.5.22}{473}{\textcolor {Chapter }{$\ast ${\nobreakspace }$S_{10}(2)$}}{subsection.11.5.22}{}}
\@writefile{brf}{\backcite{Be00}{{474}{11.5.22}{subsection.11.5.22}}}
\@writefile{brf}{\backcite{KlL90}{{474}{11.5.22}{subsection.11.5.22}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.23}\textcolor {Chapter }{$U_4(2)$}}{474}{subsection.11.5.23}\protected@file@percent }
\newlabel{U42}{{11.5.23}{474}{\textcolor {Chapter }{$U_4(2)$}}{subsection.11.5.23}{}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{475}{11.5.23}{subsection.11.5.23}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.24}\textcolor {Chapter }{$U_4(3)$}}{477}{subsection.11.5.24}\protected@file@percent }
\newlabel{U43}{{11.5.24}{477}{\textcolor {Chapter }{$U_4(3)$}}{subsection.11.5.24}{}}
\citation{CCN85}
\citation{CCN85}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{478}{11.5.24}{subsection.11.5.24}}}
\citation{CCN85}
\@writefile{brf}{\backcite{CCN85}{{479}{11.5.24}{subsection.11.5.24}}}
\@writefile{brf}{\backcite{CCN85}{{479}{11.5.24}{subsection.11.5.24}}}
\@writefile{brf}{\backcite{CCN85}{{479}{11.5.24}{subsection.11.5.24}}}
\citation{MSW94}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.25}\textcolor {Chapter }{$U_6(3)$}}{480}{subsection.11.5.25}\protected@file@percent }
\newlabel{U63}{{11.5.25}{480}{\textcolor {Chapter }{$U_6(3)$}}{subsection.11.5.25}{}}
\@writefile{brf}{\backcite{MSW94}{{480}{11.5.25}{subsection.11.5.25}}}
\citation{MSW94}
\@writefile{toc}{\contentsline {subsection}{\numberline {11.5.26}\textcolor {Chapter }{$U_8(2)$}}{481}{subsection.11.5.26}\protected@file@percent }
\newlabel{U82}{{11.5.26}{481}{\textcolor {Chapter }{$U_8(2)$}}{subsection.11.5.26}{}}
\@writefile{brf}{\backcite{MSW94}{{481}{11.5.26}{subsection.11.5.26}}}
\bibstyle{alpha}
\bibdata{../doc/manualbib.xml,gapmanualbib.xml}
\bibcite{Be00}{Ber00}
\bibcite{BG21}{BG}
\bibcite{BGK}{BGK08}
\bibcite{GMN}{BGL{$^{+}$}10}
\bibcite{BGS11}{BGS11}
\bibcite{BMO17}{BMO17}
\bibcite{BN95}{BN95}
\citation{JLPW95}
\bibcite{BP98copy}{BP98}
\bibcite{AmbigFus}{Brea}
\bibcite{ProbGenArxiv}{Breb}
\bibcite{Auto}{Brec}
\bibcite{Bre91}{Bre91}
\@writefile{brf}{\backcite{JLPW95}{{483}{11}{chapter*.3}}}
\bibcite{Bre11}{Bre11}
\bibcite{CTblLib}{Bre22}
\bibcite{BW1}{BW75}
\bibcite{CCN85}{CCN{$^{+}$}85}
\bibcite{CP96}{CP96}
\bibcite{Dad66}{Dad66}
\bibcite{DNT}{DNT13}
\bibcite{Feit82}{Fei82}
\bibcite{Gag86}{Gag86}
\bibcite{GAP}{GAP21}
\bibcite{GMS89}{GJMS89}
\bibcite{GK}{GK00}
\bibcite{GM01}{GM01}
\bibcite{GPPS}{GPPS99}
\bibcite{HL89}{HL89}
\bibcite{HL94}{HL94}
\bibcite{cohomolo}{Hol08}
\bibcite{HP89}{HP89}
\bibcite{HulpkeTG}{Hul05}
\bibcite{Hup67}{Hup67}
\bibcite{HW04}{HW04}
\bibcite{HW08}{HW08}
\bibcite{Isa76}{Isa76}
\bibcite{JLPW95}{JLPW95}
\bibcite{KlL90}{KL90}
\bibcite{Kle87}{Kle87}
\bibcite{LP10}{LP10}
\bibcite{LW91}{LW91}
\bibcite{MSW94}{MSW94}
\bibcite{Nav98}{Nav98}
\bibcite{TomLib}{NMP18}
\bibcite{AtlasImpII}{Nor}
\bibcite{NPP84}{NPP84}
\bibcite{NR14}{NR14}
\bibcite{NW02}{NW02}
\bibcite{NW12}{NW13}
\bibcite{Ost86}{Ost86}
\bibcite{Vdo00}{Vdo00}
\bibcite{Mmaxes}{Wil}
\bibcite{Wil93a}{Wil93a}
\bibcite{Wilson93}{Wil93b}
\bibcite{Wil98}{Wil98}
\bibcite{Wil99}{Wil99}
\bibcite{Wil10}{Wil10}
\bibcite{AtlasRep}{WPN{$^{+}$}19}
\bibcite{AGRv3}{WWT{$^{+}$}}
\@writefile{toc}{\contentsline {chapter}{References}{487}{chapter*.3}\protected@file@percent }
\@writefile{toc}{\contentsline {chapter}{Index}{488}{section*.4}\protected@file@percent }
