[GAP Forum] Order of elements in a group and their statistics

[Stefanos Aivazidis]

Dear forum,

I have the following (rather naive) question to ask: what is the
most efficient way to find the spectrum of a finite group G, and
compute for each integer in the spectrum the number of elements with
given order? An integer d lies in the spectrum of G iff there exists
at least one g in G such that o(g)=d.  The algorithm, I imagine, should
proceed along these lines:

1) define the group G,
2) compute the set of divisors of |G| and store this as a list L,
3) refine L (by excluding those divisors of |G| which do not
     appear as element orders) to obtain the spectrum of G and
     store this in a new list L',
4) compute how many elements of G have order d, for each d in L'

Your thoughts on how to make this precise algorithmically would
be much appreciated. Also, is it possible to produce a graph with
the statistics found by the main programme?

Many thanks in advance.

Best wishes,
Stefanos