[GAP Forum] Problem with orbits on RightTransversal

[Anvita]

Dear forum,

The first part of the following code returns a strange result:
two orbits of size 6 on a 6-element right transversal.
Shouldn't the given action coincide with the action on
the right cosets as shown in the second part of the code?

Thank you,
Anvita

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gap>
gap> S4:=SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> S3:=SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> K:=Group((1,2),(1,2)(3,4));
Group([ (1,2), (1,2)(3,4) ])
gap> RT:=RightTransversal(S4,K);
RightTransversal(Sym( [ 1 .. 4 ] ),Group([ (1,2), (1,2)(3,4) ]))
gap> ORT:=Orbits(S3,RT,OnRight);;
gap> List(ORT,Size);
[ 6, 6 ]
gap>
gap>############################################################
gap>
gap> RC:=RightCosets(S4,K);;
gap> ORC:=Orbits(S3,RC,OnRight);;
gap> List(ORC,Size);
[ 3, 3 ]
gap>
----------------------------------------------------------------


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