GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
# RepresentativeAction used to produce incorrect answers for both # symmetric and alternating groups, with both OnTuples and OnSets, by # producing elements outside the group. # This bug was originally reported by Mun See Chang. gap> RepresentativeAction(SymmetricGroup([5,7,11,15]),[7,11],[5,15],OnTuples); (5,7)(11,15) gap> RepresentativeAction(AlternatingGroup([5,7,11,15]),[7,11],[5,15],OnTuples); (5,7)(11,15) gap> RepresentativeAction(SymmetricGroup([5,7,11,15]),[7,11],[5,15],OnSets); (5,7)(11,15) gap> RepresentativeAction(AlternatingGroup([5,7,11,15]),[7,11],[5,15],OnSets); (5,7)(11,15)