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# Revision history [back]

sage: D = SymmetricGroup(4)
sage: H=D.subgroups()
sage: H[18]
Permutation Group with generators [(1,2)(3,4), (1,3,2,4)]
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[6])
sage: print(A)
{(1,4,3,2), (), (1,3,4), (2,4), (1,3,2,4), (1,2,3), (1,4,2,3), (1,2)(3,4)}
sage: D = SymmetricGroup(4)
sage: H=D.subgroups()
sage: H[18]
Permutation Group with generators [(1,2)(3,4), (1,3,2,4)]
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[6])
sage: print(A)
{(1,4,3,2), (), (1,3,4), (2,4), (1,3,2,4), (1,2,3), (1,4,2,3), (1,2)(3,4)}

Use D(x)*D(y) instead of D(x*y):

sage: D = SymmetricGroup(4)
sage: H=D.subgroups()
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[6])
sage: print(A)
{(1,4,3,2), (), (1,3,4), (2,4), (1,3,2,4), (1,2,3), (1,4,2,3), (1,2)(3,4)}
sage: A=Set(D(x)*D(y) for x in H[18] for y in H[26])
sage: print(A)
{(1,4), (1,3)(2,4), (1,3,4,2), (2,3), (3,4), (1,4,2,3), (), (2,3,4), (1,3,2,4), (1,4)(2,3), (1,4,3), (1,2,4), (1,2), (1,2)(3,4), (1,3,2), (1,2,4,3)}