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Subgroups used during the computation of the 2-modular character table of Fi23

During the computation of the 2-modular character table of the sporadic simple group Fi23 Gerhard Hiß, Felix Noeske and myself used several subgroups. This page is to document which groups were used exactly. The groups are described by GAP straight line programs in terms of standard generators for Fi23 in the sense of Rob Wilson's Atlas of Group Representations.

From this page one can download a GAP program that contains those straight line programs together with instructions for use.

GAP program fi23slps.g

Use for example as follows in GAP:

gap> LoadPackage("atlasrep");
gap> Read("fi23slps.g");
gap> gens := AtlasGenerators("Fi23",1).generators;;
gap> ngens := ResultOfStraightLineProgram(fi23_m7,gens);;
gap> kgens := ResultOfStraightLineProgram(m7_k,ngens);;
gap> sygens := ResultOfStraightLineProgram(m7_sy,ngens);;
gap> ugens := ResultOfStraightLineProgram(sy_u,sygens);;
gap> coreps := ResultOfStraightLineProgram(reps,gens);;

After that,

  • gens are generators for Fi23
  • ngens are generators for the 7th maximal subgroup N of type 31+8.21+6.31+2.2S4
  • kgens are generators for the condensation subgroup of type 31+8
  • sygens are generators for the 3-Sylow subgroup of N
  • ugens are generators for the helper subgroup U of order 6561
  • coreps are N-N-double-coset representatives in Fi23.