[GAP Forum] Computing number of isomorphism classes of finite group

[Alexander Hulpke]

Dear Moritz Schmidt,

> I was able to compute the number of isomorphism classes for quite a
> number of groups that I am interested in. The only thing that didn't
> work so far was to calculate the number of conjugacy classes of
> subgroups of the Coxeter group B_6 (which is isomorphic to O(6) \cap
> GL(6,Z)). I get the following error:
> gap> G := WreathProduct(CyclicGroup(2), SymmetricGroup(6));
> <group of size 46080 with 3 generators>
> gap> cc := ConjugacyClassesSubgroups(G);;

> Is this a bug? Or is GAP trying to say "too complicated, cannot do it"?

Yes, it is a (very insubstantial) bug which I will fix. However what triggers it is the way your group G is represented -- this also makes the overall calculation much slower -- namely as an abstract wreath product.

gap> G.1;
WreathProductElement(f1,<identity> of ...,<identity> of ...,<identity> of ...,<identity\
> of ...,<identity> of ...,())

The reason for this is that `CyclicGroup(2)' produces a PC group by default.

If you instead force a permutation group:

gap> G := WreathProduct(CyclicGroup(IsPermGroup,2), SymmetricGroup(6));
<permutation group of size 46080 with 8 generators>

The calculation should go fine.  (about 40 sec. on my system, 7440 classes)

Regards,

   Alexander Hulpke