hello gap-forum!

My problem is the following:

I try to find all the triples of generators of the two-dimensional
special linear group over a finite field (say G:= SL(2, GF(p^n))),
upto automorpism of these triples, and such that the product of the
three generators equals 1; my question is:

For a fixed finite group G (in my case a matrix group); a fixed number m
(in my case 2 or 3); and fixed numbers a1,..am (dividing Size(G)),
what is the quickest way to find, for example, the set
(1) {{g1,..,gm} \in Gx..xG| <g1,..,gm>=G and ord(gi)=ai for all i}
(2) {{g1,..,gm} \in Gx..xG| 
              <g1,..,gm>=G and g1...gm=1 and ord(gi)=ai for all i} 

or, if no function exists which returns such m-tuples given a1,..,am
(3) to find the set of ALL m-tuples of generators of G

hope someone can help me, thank you very much

Guido Helmers

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