[20, 12, [2, 2, 2, 2, 2, 2, 2, 6, 6], "possibly_metacyclic"]
[20, 12, [2, 2, 2, 2, 2, 2, 3, 3, 6], "possibly_metacyclic"]
[20, 12, [2, 2, 2, 2, 2, 2, 3, 4, 4], "possibly_metacyclic, not_abelian"]
[20, 12, [2, 2, 2, 2, 2, 3, 3, 3, 3], ""]
[20, 8, [4, 4, 4, 4, 4, 4, 4, 4, 4], ""]