[GAP Forum] Conway Co2 group

[Leonard Soicher]

Dear GAP-Forum,

On Sun, Apr 09, 2006 at 08:45:54PM -0600, Alexander Hulpke wrote:
[...] 
> Alas this is primitive, so we don't have an easy way of reducing the  
> degree of the permutation action via blocks. (In fact it is rather  
> hard to construct the representation of degree 2300 from this, which  
> makes the first approach much more promising.)
> 

It is worth pointing out that Praeger and Soicher's book, "Low Rank
Representations and Graphs for Sporadic Groups" (CUP, 1997), contains
presentations for many sporadic groups (often presentations from
the ATLAS), together with sets of words generating subgroups of low
(permutation) rank.  The given presentations and subgroup generators
seem to be "coset enumeration friendly" and can be used to construct many
low-rank representations of sporadic groups.  In particular, on page 106,
the ATLAS presentation for Co2 is given, together with sets of words (in
the generators of the given presentation) generating various subgroups,
including U6(2):2 of index 2300.

Best wishes,
Leonard Soicher