I am looking for the fastest method to decide if two
permutation groups are conjugated in a sufficiently
large symmetric group and if so to find a conjugating
permutation. Does someone know a method which does
not rely on character theory or brute force?
In other words: Given permutation groups G, H, solve
S := SymmetricGroup( Maximum( PermGroupOps.LargestMovedPoint(G), PermGroupOps.LargestMovedPoint(H) ) ); x := RepresentativeOperation( S, AsSubgroup(S, G), AsSubgroup(S, H) );
(without computing the orbit of G, of course).