[10, 12, [2, 2, 2, 2, 2, 2, 2], "not_abelian"]
[10, 10, [2, 2, 2, 2, 2, 2, 5], "possibly_metacyclic, not_abelian"]
[10, 8, [2, 2, 2, 2, 4, 4, 4], "possibly_metacyclic"]
[10, 6, [3, 3, 3, 3, 3, 6, 6], "is_cyclic"]
[10, 5, [5, 5, 5, 5, 5, 5, 5], "is_cyclic"]