Permutation set acting on another set

savecancel

Maybe something like this...

A4 = AlternatingGroup(4)
r1 = A4("(1,2) (3,4)")
r2 = A4("(1,3) (2,4)")
r3 = A4("(1,4) (2,3)")
N = A4.subgroup([r1, r2, r3]) # generate normal subgroup
LC = A4.cosets(N, side="left")

elements = []
for i in range(len(LC[0])):
    for j in range(len(LC[1])):
        elements.append( Permutation(LC[0][i]).left_action_product(Permutation(LC[1][j])) )
myset = Set(elements)
myset

Output: {[3, 1, 2, 4], [1, 3, 4, 2], [2, 4, 3, 1], [4, 2, 1, 3]}