[GAP Forum] efficient generating set for a permutation group

[Ignat Soroko]

Dear GAP experts,

I am computing a group of graph automorphisms by ad hoc methods, and have a
code (here gen is a partition of [1..n] corresponding to the degrees of
vertices):

G:=Group(Union(List(gen,x->GeneratorsOfGroup(SymmetricGroup(x)))));
aut:=[];
for g in G do
if ForAll([1..n-1],i->ForAll([i+1..n],j->m[i^g][j^g]=m[i][j])=true) then
Add(aut,g);
fi;
od;
Aut:=Group(aut);

In some situations the resulting permutation group gets a huge generating
set, like the following one:

Aut:=Group(Elements(SymmetricGroup(10)));

and all operations with it become super slow. Is there a way to make GAP
pass to a smaller generating set? Unfortunately, commands like
SmallGeneratingSet(Aut); never terminate.

Any hints?

Thank you!

Best wishes,
Ignat Soroko
https://www.math.lsu.edu/~ignatsoroko/