[17, 12, [2, 2, 2, 2, 2, 2, 2, 2, 3], "not_abelian"]
[17, 10, [2, 2, 2, 2, 2, 2, 2, 5, 10], "is_cyclic"]
[17, 8, [2, 2, 2, 4, 4, 4, 4, 4, 4], "possibly_metacyclic"]