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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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# 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)