[6, 420, [2, 3, 7], "simple_quotient, not_abelian"]

[6, 240, [2, 3, 8], "not_abelian"]

[6, 180, [2, 3, 9], "not_abelian"]

[6, 150, [2, 3, 10], "not_abelian"]

[6, 120, [2, 3, 12], "not_abelian"]

[6, 96, [2, 3, 16], "not_abelian"]

[6, 90, [2, 3, 18], "not_abelian"]

[6, 84, [2, 3, 21], "not_abelian"]

[6, 78, [2, 3, 26], "possibly_metacyclic, not_abelian"]

[6, 200, [2, 4, 5], "not_abelian"]

[6, 120, [2, 4, 6], "not_abelian"]

[6, 80, [2, 4, 8], "not_abelian"]

[6, 72, [2, 4, 9], "not_abelian"]

[6, 60, [2, 4, 12], "not_abelian"]

[6, 56, [2, 4, 14], "possibly_metacyclic, not_abelian"]

[6, 48, [2, 4, 24], "possibly_metacyclic, not_abelian"]

[6, 100, [2, 5, 5], "not_abelian"]

[6, 50, [2, 5, 10], "possibly_metacyclic, not_abelian"]

[6, 40, [2, 5, 20], "possibly_metacyclic, not_abelian"]

[6, 60, [2, 6, 6], "not_abelian"]

[6, 48, [2, 6, 8], "possibly_metacyclic, not_abelian"]

[6, 36, [2, 6, 18], "possibly_metacyclic, not_abelian"]

[6, 40, [2, 8, 8], "not_abelian"]

[6, 32, [2, 8, 16], "possibly_metacyclic, not_abelian"]

[6, 36, [2, 9, 9], "not_abelian"]

[6, 30, [2, 10, 15], "possibly_metacyclic, not_abelian"]

[6, 26, [2, 13, 26], "is_cyclic"]

[6, 28, [2, 14, 14], "possibly_metacyclic"]

[6, 24, [2, 24, 24], "is_cyclic"]

[6, 120, [3, 3, 4], "not_abelian"]

[6, 75, [3, 3, 5], "not_abelian"]

[6, 60, [3, 3, 6], "not_abelian"]

[6, 48, [3, 3, 8], "not_abelian"]

[6, 45, [3, 3, 9], "not_abelian"]

[6, 39, [3, 3, 13], "possibly_metacyclic, not_abelian"]

[6, 36, [3, 3, 18], "not_abelian"]

[6, 60, [3, 4, 4], "not_abelian"]

[6, 30, [3, 6, 6], "not_abelian"]

[6, 24, [3, 6, 12], "not_abelian"]

[6, 21, [3, 7, 21], "is_cyclic"]

[6, 24, [3, 8, 8], "possibly_metacyclic, not_abelian"]

[6, 18, [3, 18, 18], "is_cyclic"]

[6, 40, [4, 4, 4], "not_abelian"]

[6, 28, [4, 4, 7], "possibly_metacyclic, not_abelian"]

[6, 24, [4, 4, 12], "not_abelian"]

[6, 20, [4, 5, 20], "is_cyclic"]

[6, 24, [4, 6, 6], "possibly_metacyclic, not_abelian"]

[6, 16, [4, 16, 16], "is_cyclic"]

[6, 25, [5, 5, 5], "possibly_metacyclic"]

[6, 20, [5, 5, 10], "not_abelian"]

[6, 15, [5, 15, 15], "is_cyclic"]

[6, 18, [6, 6, 9], "not_abelian"]

[6, 14, [7, 14, 14], "is_cyclic"]

[6, 16, [8, 8, 8], ""]

[6, 13, [13, 13, 13], "is_cyclic"]