[GAP Forum] Conjugacy classes Alternating group degree 125

[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.