[10, 18, [2, 2, 2, 2, 2, 2], "not_abelian"]
[10, 12, [2, 2, 2, 2, 3, 6], "possibly_metacyclic"]
[10, 12, [2, 2, 2, 2, 4, 4], "not_abelian"]
[10, 10, [2, 2, 2, 2, 10, 10], "is_cyclic"]
[10, 12, [2, 2, 2, 3, 3, 3], ""]
[10, 8, [2, 4, 4, 4, 4, 4], "possibly_metacyclic"]
[10, 9, [3, 3, 3, 3, 3, 3], "possibly_metacyclic"]
[10, 6, [6, 6, 6, 6, 6, 6], "is_cyclic"]