[GAP Forum] Some GAP question

[Levie Bicua]

Dear GAP forum members,
I’m new to this GAP thing and I think this question is trivial to most of you. 
Suppose I have a set of 3 elements coming from s4 (e.g. [(1,3),(2,4),(1,2)]) and I want to generate other sets using GAP by the method below:
gap> ()^-1*[(1,3),(2,4),(1,2)]*();
[ (1,3), (2,4), (1,2) ]
gap> (2,3)^-1*[(1,3),(2,4),(1,2)]*(2,3);
[ (1,2), (3,4), (1,3) ]
gap> (2,4)^-1*[(1,3),(2,4),(1,2)]*(2,4);
[ (1,3), (2,4), (1,4) ]
gap> (3,4)^-1*[(1,3),(2,4),(1,2)]*(3,4);
[ (1,4), (2,3), (1,2) ]
gap> (2,3,4)^-1*[(1,3),(2,4),(1,2)]*(2,3,4);
[ (1,4), (2,3), (1,3) ]
gap> (2,4,3)^-1*[(1,3),(2,4),(1,2)]*(2,4,3);
[ (1,2), (3,4), (1,4) ]
The method gave 6 different sets of 3 elements. If I will use another set of 3 elements and repeat the process with again using (),(2,3),(2,4),(3,4),(2,3,4), (2,4,3) as conjugating elements, I will obtain again 6 different sets. But using this process every time I want to obtain a list of different sets as above would be eating much of my time. Is there a more efficient command/method than what I had used? Thanks.