C24 SmallGroup(24, 2)

[24 13 12 2]: [f1, f4, f1*f2, f1*f3, f1*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f1*f2^2*f3*f4]
              [2, 5, 6, 7, 8, 13, 14, 15, 16, 20, 21, 22, 24]

[24 17 16 10]: [f2, f4, f1*f2, f2^2, f2*f3, f2*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
               [3, 5, 6, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24]

[24 19 18 14]: [f1, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f3*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f3, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
               [2, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24]

[24 21 20 18]: [f1, f2, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
               [2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]