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Dear GAP-forum,

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

the problem

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).

Sebastian Egner.

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