[GAP Forum] Maximal Subgroups for O(7,3)

Joe Bohanon jbohanon2 at gmail.com
Thu Nov 13 05:37:37 GMT 2008

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


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.


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