[GAP Forum] 3.M_{22}:2 on 990 points

[dmitrii.pasechnik at cs.ox.ac.uk]

On Tue, Nov 15, 2016 at 10:16:36PM +0100, Juergen Mueller wrote:
> Dear Robert,
> 
> here is essentially how I did it:
> 
> (The generators this produces are different from the ones
> I sent earlier, because the details of the constructions differ.)
> 
> #####
> 
> # finds generators of 2x2^3:L3(2) inside M22.2
> slp:=AtlasStraightLineProgram("M22.2",5).program;
> 
> # 3.M22.2 in dimension 12, std.gens. lifting those of M22.2
> gens:=AtlasGenerators("3.M22.2",1).generators;
> 
> # a subgroup of 3.(2x2^3:L3(2)) projecting onto 2x2^3:L3(2)
> hgens:=ResultOfStraightLineProgram(slp,gens);
> 
> # indeed 2x2^3:L3(2)
> g:=Group(gens); h:=Group(hgens); Size(h);
> 
> # go over to perm.rep, actually on 693 points
> iso:=IsomorphismPermGroup(g); LargestMovedPointPerm(gg);
> gg:=Image(iso,g); hh:=Image(iso,h);
> 
> # action on cosets
> cos:=RightCosets(gg,hh); Length(cos); 
> act:=Action(gg,cos,OnRight); LargestMovedPointPerm(act);

That's more or less what I outlined in my message - 
2x2^3:L3(2) is the stabiliser of a 7-clique in the 693-vertex
graph. It's computationally faster to create the orbit of 990 7-subsets,
but OK, that mattered a lot 25+ years ago, when that graph was
constructed :-)

Just in case,
Dima

> 
> #####
> 
> Best wishes, Jürgen
> 
> 
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