[GAP Forum] Conway Co2 group

[Sven Reichard]

Rudolf,

you can get a permutation representation of Co2 on 2300 points from the 
AtlasRep package. This representation can be dealt with quite efficiently.

gap> LoadPackage("atlasrep");
-----------------------------------------------------------------------------
Loading  AtlasRep 1.2.1 (An Atlas of Group Representations)
by Robert A. Wilson (http://for.mat.bham.ac.uk/R.A.Wilson),
    Richard A. Parker (http://www.ukonline.co.uk/richard),
    John Bray (http://web.mat.bham.ac.uk/J.N.Bray), and
    Thomas Breuer (http://www.math.rwth-aachen.de/~Thomas.Breuer).
-----------------------------------------------------------------------------
true
gap> DisplayAtlasInfo("Co2", IsPermGroup);
Representations for G = Co2:    (all refer to std. generators 1)
----------------------------
1: G <= Sym(2300)
2: G <= Sym(4600)
gap> gens := AtlasGenerators("Co2", 1).generators;;
gap> G := Group(gens);
<permutation group with 2 generators>
gap> Size(G);
42305421312000

If you want an FP group, you may also try a shorter set of generators, 
found on the Atlas Homepage:
< a, b | a^2 = b^5 = (ab^2)^9 = [a, b]^4 = [a, b^2]^4 = [a, bab]^3 = [a, 
bab^2ab]^2 = [a, bab^-2]^3 = [a, b^-2abab^-2]^2 = (abab^2ab^-1ab^-2)^7 = 
1 >.

Hope this helps,
Sven Reichard.