If I have two particular subgroups of a symmetric group, is there any built-in way in Sage to determine if the groups are conjugate to one another? I tried creating a ConjugacyClass for each and then comparing them, but this gives an error:
S = SymmetricGroup(3)
gen1 = Permutation('(1,2,3)')
gen2 = Permutation('(1,3,2)')
gen3 = Permutation('(1,2)')
gen4 = Permutation('(1,3)')
G1 = PermutationGroup([gen1, gen3])
G2 = PermutationGroup([gen2, gen4])
ConjugacyClass(S, G1) == ConjugacyClass(S, G2)
When executing the very last line I get the error
TypeError: For implementing multiplication, provide the method '_mul_' for (1,2) resp. Permutation Group with generators [(1,2), (1,2,3)]
