[GAP Forum] Modified ConjugacyClassesSubgroups?
hulpke at math.colostate.edu
Thu Oct 9 19:08:32 BST 2008
Joe Bohanon asked:
> I have a group G and a subgroup H. I want to compute the conjugacy
> classes of subgroups H where conjugacy is taken in G, instead of H.
> The way I've been doing it is the following:
> Then I manually check to see how which classes are fused in G and
> remove redundacies.
> Is there a way to get the same results without doing that? In other
> words, could I use the cyclic extension method, except compute the
> zuppos of H as conjugacy classes of G and do all the required
> calculations in G instead of H?
You can do so by explicitly calling the cyclic extension method, this
lets you apply a further filter function. For example:
Sym( [ 1 .. 7 ] )
Group([ (1,3,2), (2,4,3), (3,4,5), (1,5,6,4,3), (1,3,6,7,5) ])
function( i ) ... end
<subgroup lattice of Sym( [ 1 .. 7 ] ), 37 classes,
3786 subgroups, restricted under further condition l!.func>
# check in a naive way
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