[5, 16, [2, 2, 2, 2, 2], ""]
[5, 12, [2, 2, 2, 2, 3], "not_abelian"]
[5, 10, [2, 2, 2, 2, 5], "possibly_metacyclic, not_abelian"]
[5, 8, [2, 2, 2, 4, 4], "possibly_metacyclic"]
[5, 6, [2, 2, 3, 6, 6], "is_cyclic"]
[5, 6, [2, 3, 3, 3, 6], "is_cyclic"]
[5, 6, [3, 3, 3, 3, 3], "not_abelian"]