[GAP Forum] Conjugacy classes Alternating group degree 125

[Benjamin Sambale]

If I understand the question correctly, there is no need to use a 
computer. The conjugacy classes of the alternating groups are well-known 
and there sizes can be computed easily. But maybe this is not the point 
of the question.

Best,
Benjamin

Am 26.11.2016 um 16:17 schrieb Víctor Manuel Ortiz Sotomayor:
> Let G:=AlternatingGroup(125) be the Alternating group of degree 125, 
> and let Q:=SylowSubgroup(G, 5) be a Sylow 5-subgroup of G.
>
> I want to compute, for each element x of Q, the distinct G-conjugacy 
> class sizes, that is, the distinct values of Size(ConjugacyClass(G, 
> x)) (obviously, computing the distinct values of Centralizer(G, x) for 
> all x in Q) would be the same).
>
> Needless to say that, I always get out of memory when I run over all 
> the elements of Q. I had tried the following: compute the upper 
> central series of Q (L:=UpperCentralSeriesOfGroup(Q)) and, for some 
> "intermediate" normal subgroup N in that chain, to decompose Q in 
> right cosets on N, in order to make a disjoint union of the elements 
> of Q that is more manageable. However, I still have problems of memory 
> because either I have so many transversals or the order of N is also 
> too large. Any idea?
>
> Thanks in advance.
>
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