[GAP Forum] permutation actions

[konygin at imm.uran.ru]

Dear GAP-forum,

I have the following question:


Let G be a group generated by permutations g_1, ..., g_d on the set {1,
..., n} and H be a subgroup of G generated by permutations h_1, ..., h_k
on the set {1, ..., n} (g_1, ..., g_d, h_1, ..., h_k are given
explicitly).

Can I use GAP to get the natural (permutation) action of g_1, ..., g_d on
left cosets of G by H (ordering in some way)?

For example,
 g_1 = (1 2 3 4 5 6),
 g_2 = (1 2),
 h_1 = g_1 = (1 2),
 h_2 = (1 3)(2 4),
 h_3 = (1 3 5)(2 4 6).


Best regards,
Anton Konygin