  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThis manual describes the [5XRepsn[105X package for computing matrix representations
  in characteristic zero of finite groups. Most of the functions in [5XRepsn[105X have
  been  written  according  to  the  algorithm  described in the author's Ph.D
  thesis [DA03] and [DD10] (see [DA05]).[133X
  
  [33X[0;0YFor  constructing  representations  of simple groups and their covers we use
  the algorithm described in [Dix93]. To use this algorithm for constructing a
  representation  of  a  group [22XG[122X affording an irreducible character [22Xχ[122X of [22XG[122X, we
  need  to  have  a  subgroup [22XH[122X of [22XG[122X such that the restriction of [22Xχ[122X to [22XH[122X has a
  linear  constituent  with  multiplicity  one.  In  this  case  we say [22XH[122X is a
  [13Xcharacter  subgroup[113X  relative  to [22Xχ[122X (or a [22Xχ[122X-subgroup). A [22Xχ[122X-subgroup for each
  irreducible  character  [22Xχ[122X of degree less than 100 of simple groups and their
  covers are listed in [DA06] and [DA07].[133X
  
  [33X[0;0YAll  [5XRepsn[105X  functions are written entirely in the [5XGAP[105X language. It is proved
  in  [DA05]  and  [DD10]  that  the algorithm is correct for any group with a
  character  of  degree less than 100. Indeed, if the group is solvable, there
  is  no restriction on the character degree. In practice the program is quite
  fast  when the degree is small, but can be very slow when it is necessary to
  call one of the subprograms which extend irreducible representations. In the
  latter  case  the  number  of  element  wise operations required to extend a
  representation of degree [22Xd[122X is proportional to [22Xd^6[122X.[133X
  
  [33X[0;0Y[5XRepsn[105X  is implemented in the [5XGAP[105X language, and runs on any system supporting
  [5XGAP[105X4.  The  [5XRepsn[105X  package  is  loaded into the current [5XGAP[105X session with the
  command[133X
  
   gap> LoadPackage( "repsn" ); 
  
  [33X[0;0Y(see section [13XLoading a GAP Package[113X in the [5XGAP[105X Reference Manual).[133X
  
  [33X[0;0YPlease  report  any  bugs  or other issues you might encounter via the [5XRepsn[105X
  issue tracker at [7Xhttps://github.com/gap-packages/repsn/issues[107X.[133X
  
