
<!-- %W  introduc.xml    GAP 4 package CTblLib              Thomas Breuer -->
<!-- %Y  Copyright 2011, Lehrstuhl D für Mathematik, RWTH Aachen, Germany -->


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Chapter Label="ch:introduction">
<Heading>Introduction to the &GAP; Character Table Library</Heading>

The usefulness of &GAP; for character theoretic tasks depends on the
availability of many known character tables,
and there are a lot of character tables in the &GAP; table library.
Of course, this library is <Q>open</Q> in the sense that it shall be extended.
So we would be grateful for any further tables of interest
sent to us for inclusion into our library.
Please offer interesting new character tables via e-mail
to &AUTHOREMAIL;.

<P/>

It depends on your &GAP; installation whether the character table library
is available.
You can check this as follows.

<P/>

<Example><![CDATA[
gap> InstalledPackageVersion( "ctbllib" ) <> fail;
true
]]></Example>

<P/>

If the result is <K>false</K> then the library is not installed,
and you may ask your system administrator for installing it,
or install the library in your home directory,
see Section&nbsp;<Ref Subsect="subsect:install"/>.

<P/>

For general information about character tables in &GAP;,
see Chapter&nbsp;<Ref Chap="Character Tables" BookName="ref"/>.

<P/>

The <F>doc</F> and <F>htm</F> directories of the
&GAP; Character Table Library contain several files
with examples of character theoretic computations,
in PDF and HTML format.
<Alt Only="HTML">
<![CDATA[
<a name="application_files">Currently these are</a>
]]>
</Alt>
<Alt Not="HTML">
Currently these are
</Alt>

<P/>

<List>
  <Item>
    Ambiguous class fusions, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ambigfus.pdf</Link>
    <LinkText><F>doc/ambigfus.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ambigfus.htm</Link>
    <LinkText><F>htm/ambigfus.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Constructions of character tables using table automorphisms, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblcons.pdf</Link>
    <LinkText><F>doc/ctblcons.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblcons.htm</Link>
    <LinkText><F>htm/ctblcons.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Ordinary character tables, Brauer tables, and decomposition matrices, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldeco.pdf</Link>
    <LinkText><F>doc/ctbldeco.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctbldeco.htm</Link>
    <LinkText><F>htm/ctbldeco.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Constructing the irreducible characters of <M>J_4</M> from one
    faithful character, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblj4.pdf</Link>
    <LinkText><F>doc/ctblj4.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblj4.htm</Link>
    <LinkText><F>htm/ctblj4.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Computations of possible permutation characters, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctblpope.pdf</Link>
    <LinkText><F>doc/ctblpope.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctblpope.htm</Link>
    <LinkText><F>htm/ctblpope.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Computations of common central extensions, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctocenex.pdf</Link>
    <LinkText><F>doc/ctocenex.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/ctocenex.htm</Link>
    <LinkText><F>htm/ctocenex.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Some computations concerning the classification of groups with the
    property that all complex irreducible characters of the same degree are
    Galois conjugate (together with Klaus Lux), see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/dntgap.pdf</Link>
    <LinkText><F>doc/dntgap.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/dntgap.htm</Link>
    <LinkText><F>htm/dntgap.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Hamiltonian cycles in the generating graphs of finite groups, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/hamilcyc.pdf</Link>
    <LinkText><F>doc/hamilcyc.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/hamilcyc.htm</Link>
    <LinkText><F>htm/hamilcyc.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Multiplicity-free permutation characters of the sporadic simple groups
    and their automorphism groups, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfree.pdf</Link>
    <LinkText><F>doc/multfree.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfree.htm</Link>
    <LinkText><F>htm/multfree.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Multiplicity-free permutation characters of central extensions of
    the sporadic simple groups, and their automorphic extensions
    (together with Jürgen Müller), see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/multfre2.pdf</Link>
    <LinkText><F>doc/multfre2.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/multfre2.htm</Link>
    <LinkText><F>htm/multfre2.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    A question about the group PSO<M>^+(8,5).S_3</M>, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/o8p2s3_o8p5s3.pdf</Link>
    <LinkText><F>doc/o8p2s3_o8p5s3.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/o8p2s3_o8p5s3.htm</Link>
    <LinkText><F>htm/o8p2s3_o8p5s3.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Probabilistic generation of finite simple groups, see
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/probgen.pdf</Link>
    <LinkText><F>doc/probgen.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/probgen.htm</Link>
    <LinkText><F>htm/probgen.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Solvable subgroups of maximal order in sporadic simple groups
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/sporsolv.pdf</Link>
    <LinkText><F>doc/sporsolv.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/sporsolv.htm</Link>
    <LinkText><F>htm/sporsolv.htm</F></LinkText>
    </URL>.
  </Item>
  <Item>
    Maintenance issues concerning the &GAP; Character Table Library
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/maintain.pdf</Link>
    <LinkText><F>doc/maintain.pdf</F></LinkText>
    </URL>
    and
    <URL>
    <Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/htm/maintain.htm</Link>
    <LinkText><F>htm/maintain.htm</F></LinkText>
    </URL>.
  </Item>
</List>

<P/>

If you use the &GAP; Character Table Library to solve a problem then
please send a short e-mail to &AUTHOREMAIL; about it.
The &GAP; Character Table Library database should be referenced
as follows.

<Listing>
@misc{ CTblLib&VERSIONNUMBER;,
  author =       {Breuer, T.},
  title =        {The \textsf{GAP} {C}haracter {T}able {L}ibrary,
                  {V}ersion &VERSIONNUMBER;},
  month =        {&RELEASEMONTH;},
  year =         {&RELEASEYEAR;},
  note =         {\textsf{GAP} package},
  howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/ctbllib}
}
</Listing>

<P/>

For referencing the &GAP; system in general,
use the entry&nbsp;<Cite Key="GAP"/> in the bibliography of this manual,
see also
<P/>
<URL>http://www.gap-system.org</URL>.


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:history">
<Heading>History of the &GAP; Character Table Library</Heading>

The first version of the &GAP; Character Table Library was released with
&GAP;&nbsp;3.1 in March 1992.

<P/>

It was the first aim of this library to continue the character table library
of the &CAS; system (see <Cite Key="NPP84"/>) in &GAP;,
as a part of the process of reimplementing the algorithms of &CAS; in &GAP;,
see&nbsp;<Ref Sect="History of Character Theory Stuff in GAP"
BookName="ref"/>.
&GAP;&nbsp;3.1 provided only very restricted methods for computing character
tables from groups,
so its character theory part was concerned mainly with library tables.

<P/>

A second aspect of the character table library was to make all character
tables shown in the &ATLAS; of Finite Groups
<Cite Key="CCN85"/> available in &GAP;.
In fact &GAP; turned out to provide a very good environment for
systematic checks of these character tables.

<P/>

To some extent,
the access to the (ordinary) character tables in&nbsp;<Cite Key="CCN85"/>
was a prerequisite for storing also the corresponding Brauer character tables
in the &GAP; Character Table Library.
Already &GAP;&nbsp;3.1 contained many of these tables.
They have been computed mainly <Q>outside of &GAP;</Q>,
using the methods described in&nbsp;<Cite Key="HJLP92"/>,
and part of the library has been published in the &ATLAS;
of Brauer Characters <Cite Key="JLPW95"/>.
One of the roles of &GAP; was again to perform systematic checks.

<P/>

Besides these projects, many individual character tables have been added
to the &GAP; Character Table Library since the times of &GAP;&nbsp;3.1.
They were computed from groups or with character theoretic methods
or using a combination of these two possibilities
(see, e.&nbsp;g., <Cite Key="NPP84"/> and <Cite Key="LP91"/>).

<P/>

Section&nbsp;<Ref Sect="sec:contents"/> lists some of the sources.
The changes in the &GAP; Character Table Library since the release of
&GAP;&nbsp;4.1 (in July 1999) are individually documented in the file
<URL>
<Link>http://www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/doc/ctbldiff.pdf</Link>
<LinkText><F>doc/ctbldiff.pdf</F></LinkText>
</URL> of the package.

<P/>

Currently the main focus in the development of the &GAP; Character Table
Library is
&ndash;besides the addition of tables that appear to be interesting&ndash;
the better interaction with other databases,
such as the &ATLAS; of Group Representations and the
&GAP; Library of Tables of Marks 
(see the &GAP; packages <Package>AtlasRep</Package> and
<Package>TomLib</Package>)
and &GAP;'s group libraries,
and an improvement of the <Q>database</Q> aspect
of the character table library itself,
see the sections <Ref Sect="sect:accessdata"/> and
<Ref Sect="sect:ctbllib-browse"/>.

<!-- mention also the <Q>WWW table of contents</Q> -->

<P/>

Until the release of &GAP;&nbsp;4.3 in spring 2002,
the &GAP; Character Table Library had been a part of the main &GAP;
library.
With &GAP;&nbsp;4.3, it was <Q>split off</Q> as a &GAP; package.

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sect:What's New in CTblLib?">
<Heading>What's New in <Package>CTblLib</Package>,
Compared to Older Versions?</Heading>

<!-- The section title is referenced in index.html. -->
<Alt Only="HTML"><![CDATA[<a id="sect:news"/>]]></Alt>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.2">
<Heading>What's New in Version 1.2?</Heading>

The following bugs were fixed in version 1.2.2.

<List>
<Item>
  The functions <Ref Func="AllCharacterTableNames"/> and
  <Ref Func="OneCharacterTableName"/> ran into an error in certain situations,
  if the library had been extended by private tables,
  see Section <Ref Sect="sec:extending"/>.
  (As a consequence, the description of <Ref Prop="IsDuplicateTable"/>
  has been extended.)
  Thanks to Alexander Konovalov and Lukas Maas for pointing out this error.
</Item>
<Item>
  The function <Ref Func="CharacterTableOfIndexTwoSubdirectProduct"/>
  returned a wrong result if the two factors were given by the same
  character table, for example in the case of <M>(A_5 \times A_5).2</M>
  created as a subdirect product of two copies of <M>S_5</M>.
</Item>
</List>

<P/>

Concerning character table data, we have the following.

<List>
<Item>
  A few bugs in character tables have been fixed.
</Item>
<Item>
  Several class fusions stored in character tables have been changed,
  in order to be more consistent with related data,
  see Section <Ref Sect="sec:CTblLib Maintenance"/> for reasons of such
  changes.
</Item>
<Item>
  Many new character tables have been added.
  For example, a character table is available for each table of marks in the
  <Package>TomLib</Package> package.
</Item>
</List>

Like in earlier versions, the PDF file <F>doc/ctbldiff.pdf</F> of the package
lists the important changes, mainly related to the relevant simple groups.
However, a probably more suitable overview is given by the &GAP; readable
file <F>data/ctbldiff.dat</F>, which contains a complete overview of all
changes, including the additions of class fusions.
(Note that each added or changed fusion is mentioned twice in this list,
once for the <Q>from</Q> table and once for the <Q>to</Q> table.)
This list of changes can be shown using
<Ref Func="BrowseCTblLibDifferences"/>
if the <Package>Browse</Package> package (see&nbsp;<Cite Key="Browse"/>)
is available.

<P/>

Besides these changes of the data, the following features are new.

<List>
<Item>
  A tutorial for beginners was added to the package manual,
  see Chapter <Ref Chap="ch:tutorial"/>,
  and the package manual was restructured.
  The manual is now based on the <Package>GAPDoc</Package> package.
</Item>
<Item>
  Generic constructions of Brauer tables are now available if the
  underlying ordinary table is encoded via <Ref Func="ConstructMGA"/>,
  <Ref Func="ConstructIndexTwoSubdirectProduct"/>, or
  <Ref Func="ConstructV4G"/>,
  and if the Brauer tables of the compound tables are known.
</Item>
<Item>
  The attributes <Ref Attr="FusionToTom"/> and <Ref Attr="Maxes"/> are no
  longer set in duplicate tables.
  This can be regarded as a bugfix, in the following sense.
  For the sake of consistency, it would in general be necessary
  to apply a permutation to the fusion into the table of marks,
  and to add the class fusions from the tables of the maximal subgroups to
  the duplicate table.
</Item>
<Item>
  The consistency checks for character tables have been improved
  and are now documented,
  see Section&nbsp;<Ref Sect="sec:CTblLib Sanity Checks"/>.
  Due to these checks, several class fusions had to be replaced.
</Item>
<Item>
  The concept of duplicate character tables is now explicit,
  see Section&nbsp;<Ref Sect="sec:duplicates"/>.
  As a consequence, the behaviour of <Ref Func="AllCharacterTableNames"/>
  has changed in situations where <C>IsSimple</C> and <C>IsSporadicSimple</C>
  (see <Ref Subsect="Group Operations Applicable to Character Tables"
  BookName="ref"/>) occur, as follows.
  In earlier versions of the package, duplicate tables had automatically been
  excluded.  From now on, duplicates can be excluded if one wants so,
  but they are not automatically excluded.
  This change may be regarded as a bugfix.
</Item>
<Item>
  Several attribute values for character tables,
  such as <Ref Attr="Size" BookName="ref"/> and
  <Ref Attr="NrConjugacyClasses" BookName="ref"/> are now available
  without reading the character table data files,
  provided that the <Package>Browse</Package> package
  (see&nbsp;<Cite Key="Browse"/>) has been loaded.
  See the documentation of <Ref Func="AllCharacterTableNames"/> for details;
  this function is much faster if only these attributes appear in the
  conditions given.
  Thus it is now more reasonable to use this function
  for searches in the table library.
</Item>
<Item>
  &GAP;'s group libraries provide many groups for which the Character Table
  Library contains the character tables.
  Given a character table from the library, one can list and access
  available groups with the functions described in
  Section&nbsp;<Ref Sect="sect:tblgrp"/>,
  provided that the <Package>Browse</Package> package
  (see&nbsp;<Cite Key="Browse"/>) has been loaded.
</Item>
<Item>
  An interactive overview of the contents is now available
  that is based on the <Package>Browse</Package> package
  <Cite Key="Browse"/>,
  see Section <Ref Sect="sect:ctbllib-browse"/>.
</Item>
<Item>
  Information about Deligne-Lusztig names of unipotent characters of finite
  groups of Lie type is now available,
  see Section <Ref Sect="sec:unipotsec"/>.
</Item>
<Item>
  An interface for reading <Package>Magma</Package> tables was added,
  see Section <Ref Sect="sec:interface-magma"/>.
</Item>
</List>

</Subsection>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Subsection Label="sec:new1.1">
<Heading>What's New in Version 1.1?</Heading>

First of all, of course several character tables were added; for an overview,
see the file <F>doc/ctbldiff.pdf</F> in the home directory of the package.
Also lots of class fusions were added.
This includes factor fusions onto the tables of the factor groups modulo the
largest normal <M>p</M>-subgroups whenever the tables of the factors are
available;
these maps admit the automatic construction of the <M>p</M>-modular
Brauer tables if the corresponding tables of the factors are available.
For example, the <M>2</M>-modular Brauer table of the maximal subgroup of the
type <M>2^{10}:M_{22}</M> in the group <M>Fi_{22}</M> is available
because of the known <M>2</M>-modular table of <M>M_{22}</M>
and the stored factor fusion onto the table of <M>M_{22}</M>.

<P/>

Second, more information has been made more explicit, in the following sense.

<List>
<Item>
  <Ref Attr="Identifier" Label="for character tables" BookName="ref"/>
  values of tables that are constructed from generic tables are now valid
  arguments of <Ref Func="CharacterTable" BookName="ref"/>,
  for example <C>CharacterTable( "C10" )</C>
  and <C>CharacterTable( "Sym(5)" )</C>
  can be used to create the character table of the cyclic group of order
  <M>10</M> and of the symmetric group of degree <M>5</M>, respectively.
</Item>
<Item>
  Attributes have been introduced that replace more or less hidden
  components (see Section&nbsp;<Ref Sect="sec:attributes"/>);
  in particular, the way how many ordinary tables are encoded
  via the construction from other tables is no longer encapsulated
  in a function call but instead the name of the function and the
  arguments are stored as an attribute value
  (see&nbsp;<Ref Func="ConstructionInfoCharacterTable"/>).
</Item>
<Item>
  The functions that are used for the table constructions have been
  documented (see Chapter&nbsp;<Ref Chap="chap:constructions"/>).
</Item>
<Item>
  Several consistency checks are now part of the package distribution,
  in the files <F>gap4/test.gd</F> and <F>gap4/test.gi</F>.
  However, currently they are not documented.
  The new file <F>tst/testall.g</F> lists the files that belong to the
  <Q>standard test suite</Q>.
  Further checks involving the &GAP; Character Table Library are parts
  of the &GAP; packages AtlasRep (see&nbsp;<Cite Key="AtlasRep"/>) and TomLib.
</Item>
<Item>
  As a part of the consistency checks, class fusions between character
  tables and from character tables into corresponding tables of marks
  have been recomputed, and the <C>text</C> components have been standardized;
  this means that the texts express whether the maps are unique, unique
  up to table automorphisms, or ambiguous.
  However, currently this is not documented.
</Item>
<Item>
  One can now avoid unloading the contents of data files, which can speed
  up computations involving many library tables.
  (In version 1.1, the function <C>CTblLibSetUnload</C> had been provided
  for that.  Since version 1.2, a &GAP; 4.5 user preference replaces this
  function.)
</Item>
</List>

<P/>

Third, several errors have been corrected
(again see&nbsp;<F>doc/ctbldiff.pdf</F>).
Most of them affect class fusions, and for most of those,
the term <Q>error</Q> could be regarded as not really appropriate.
See <Ref Sect="sec:CTblLib Maintenance"/> for details.

<P/>

Finally, the &GAP; functions for reading and writing other formats of
character tables have been moved from the main &GAP; library to this package
(see Chapter&nbsp;<Ref Chap="chap:interfaces"/>),
because they are useful only for library tables.
The &GAP;&nbsp;3 format is now also supported, mainly for documentation
purposes (see Section&nbsp;<Ref Sect="sec:interface-gap3"/>).

</Subsection>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sec:acknowledgements">
<Heading>Acknowledgements</Heading>

The development of the &GAP; Character Table Library has been supported
by several DFG grants,
in particular the project
<Q>Representation Theory of Finite Groups and Finite Dimensional Algebras</Q>
(until 1991),
and the Schwerpunkt <Q>Algorithmische Zahlentheorie und Algebra</Q>
(from 1991 until 1997).

<P/>

The functions for the conversion of &CAS; tables
to &GAP; format have been written by Götz Pfeiffer.
The functions for converting the so-called <Q>Cambridge format</Q>
(in which the original data of the &ATLAS; of Finite Groups had been stored)
to &GAP; format have been written by Christoph Jansen.

<P/>

The generic character tables of double covers of alternating and
symmetric groups were contributed by Felix Noeske,
see&nbsp;<Cite Key="Noe02"/>.

<P/>

The functions in Section&nbsp;<Ref Sect="sec:unipotsec"/>
(<Ref Func="DeligneLusztigName"/>, <Ref Func="DeligneLusztigNames"/>,
and <Ref Func="UnipotentCharacter"/>)
as well as the corresponding data for the finite groups of Lie type
in the &GAP; Character Table Library
have been contributed by Michael Claßen-Houben, see&nbsp;<Cite Key="Cla05"/>.

<P/>

Several character tables of maximal subgroups of covering groups of
simple groups have been computed by Sebastian Dany,
see&nbsp;<Cite Key="Dan06"/>.
<!-- now complete: maxes of 2.A5, A9, 2.A9, A10, 2.A10, ... -->

<P/>

Thanks to Frank Lübeck and Max Neunhöffer for
their help with solving technical problems concerning the HMTL part of the
example files that belong to the package documentation,
and to Ian Hutchinson whose &TeX; to HTML translator <C>TtH</C> was used to
provide these HTML files.

<P/>

Thanks to Frank Lübeck and Max Neunhöffer also for developing the
<Package>GAPDoc</Package> package,
on which the manual of the &CTblLib; package is based.
The previously available documentation format had been completely
inappropriate.

</Section>
</Chapter>

<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->

