[6, 10, [2, 2, 2, 2, 2, 2], "not_abelian"]
[6, 8, [2, 2, 2, 2, 2, 4], "possibly_metacyclic, not_abelian"]
[6, 6, [2, 2, 2, 2, 6, 6], "is_cyclic"]
[6, 6, [2, 2, 2, 3, 3, 6], "is_cyclic"]
[6, 6, [2, 2, 3, 3, 3, 3], "possibly_cyclic, possibly_metacyclic"]
[6, 4, [4, 4, 4, 4, 4, 4], "is_cyclic"]