[GAP Forum] Maximal Subgroups for O(7,3)
jbohanon2 at gmail.com
Thu Nov 13 08:05:57 GMT 2008
Thanks. I think I see what I was doing wrong. I'm still a bit
perplexed as to why taking a random sample of 2- and 3-elements about
2000 times never produced a group in the other conjugacy class.
Asst. Prof. Dmitrii (Dima) Pasechnik wrote:
> Dear Joe,
> I don't grok your GAP code, but the GAP generators from
> are correct:
> enter them into GAP under the names given there:
> #and then do
> [ 702, 378 ]
> you see that you get different classes (if they were the same, Group(gg) would
> fix a point)
> if you know a representative H of G_2(3) in the original generators, a
> representative of the other class can be constructed by applying an
> outer automorphism to H.
> 2008/11/13 Joe Bohanon <jbohanon2 at gmail.com>:
>> 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
>> 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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