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