[GAP Forum] A question

[Sara Yaftian]

Dear Dima

Thank you very much for your complete solution.

Best regards
Sara

P.S.>I am also very thankful from Professor Stefan Kohl for his help.

On Sun, Dec 6, 2015 at 2:30 PM, Dima Pasechnik <
dmitrii.pasechnik at cs.ox.ac.uk> wrote:

> 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
>