[7, 12, [2, 2, 2, 2, 2, 2], "not_abelian"]
[7, 8, [2, 2, 2, 2, 4, 4], "possibly_metacyclic"]
[7, 6, [2, 2, 3, 3, 6, 6], "is_cyclic"]
[7, 6, [2, 3, 3, 3, 3, 6], "is_cyclic"]
[7, 6, [3, 3, 3, 3, 3, 3], "not_abelian"]