You can use:
gap> g:=AtlasGroup("O7(3)",NrMovedPoints,1080);;
gap> a:=AutomorphismGroup(g);;
Time of last command: 16073 ms
gap> h:=Stabilizer(g,1);;
gap> f:=First(GeneratorsOfGroup(a),f->NrMovedPoints(Image(f,h))=1080);;
gap> k:=Image(f,h);;
gap> chi1:=PermutationCharacter(g,h);;
Time of last command: 3636 ms
gap> chi2:=PermutationCharacter(g,k);;
Time of last command: 12641 ms
gap> chi1=chi2;
false
The paper atlas mentions that these two maximals fuse in the
automorphism group, so you know something like this should work. The
two conjugacy classes should occur equally often if you are sampling
randomly, so your method should have worked, but this is a simple
direct method.
On 2008-11-13, at 00:37, Joe Bohanon wrote:
Sorry to those of you who get this twice. I accidentally sent it to
the group pub forum first.
I'm trying to get the maximal subgroups for O(7,3) and having some
trouble. ATLAS 3.0 does not have them listed, but ATLAS 2.0 does
have the shape and there are 7 permutation representations that can
be called up by atlasrep. For each of those seven, I did the
following with G set as the smallest permrep
H:=Group(AtlasGenerators("O7(3)",i).generators);
iso:=IsomorphismGroups(H,G);
S:=Stabilizer(H,1);
Then I simply ran Image(iso,S) to get the maximals corresponding to
the primitive permreps. However for the two classes of G2(3), this
yields conjugate maximal subgroups.
In addition, I also tried to take random elements of order 2 and 3
and try to generate a G2(3), and while I was able to create many of
them, none of them were out of this one conjugacy class.
Am I missing something here? I don't think there is a mistake
anywhere, as G2(3) is listed as having two classes in Kleidman's
tables.
Thanks
Joe
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