[9, 8, [2, 2, 2, 2, 2, 4, 4], "possibly_metacyclic"]
[9, 6, [2, 3, 3, 3, 3, 3, 6], "is_cyclic"]
[9, 6, [3, 3, 3, 3, 3, 3, 3], "not_abelian"]