[GAP Forum] A question

[Dima Pasechnik]

On Sun, Dec 06, 2015 at 09:42:30AM +0330, Sara Yaftian wrote:
> I need to all partitions of the conjugacy classes of a finite group.
> GAP computes all partitions of {1,...,n}.
> How can I do that?

I suppose you would like to get all partitions of the set
of conjugacy classes. GAP has a command PartitionsSet
that (almost) does this - it needs an extra parameter, 
the number of parts.
So you can do the following:

c:=Set(ConjugacyClasses(SymmetricGroup(5))); # or some other group
[ ()^G, (1,2)^G, (1,2,3)^G, (1,2)(3,4)^G, (1,2,3,4)^G, (1,2,3)(4,5)^G, (1,2,3,4,5)^G ]
l:=List([1..Length(c)], x->PartitionsSet(c,x));;

This is already quite a big list:
gap> List(l,Length);
[ 1, 63, 301, 350, 140, 21, 1 ]

Hope this helps,
Dima