Conjugacy class of a tuple in GAP

Question

I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically).

I know that for unidimensional cases I can use IsConjugate or ConjugacyClass, but I don't know how to do for a list of elements.

Answer 1

To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:

RepresentativeAction(group,tuple1,tuple2,OnTuples);

e.g.

gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)