[8, 14, [2, 2, 2, 2, 2, 2], "not_abelian"]
[8, 12, [2, 2, 2, 2, 2, 3], "not_abelian"]
[8, 8, [2, 2, 2, 2, 8, 8], "is_cyclic"]
[8, 8, [2, 2, 2, 4, 4, 4], "possibly_metacyclic"]
[8, 6, [3, 3, 3, 3, 6, 6], "is_cyclic"]
[8, 5, [5, 5, 5, 5, 5, 5], "is_cyclic"]