CommonTransversal( G, H )
The existence of a common transversal for the left and right cosets of a subgroup H of G is a special case of systems of common representatives.
gap> T := CommonTransversal( a4, c3 );
[ (), (1,3)(2,4), (1,2)(3,4), (1,4)(2,3) ]
GAP 3.4.4