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

[Juergen Mueller]

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);

#####

Best wishes, Jürgen