S4 SmallGroup(24, 12)

[24 8 4 2]: [f3, f1*f2, f2*f3, f1*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
            [4, 6, 10, 16, 20, 21, 23, 24]

[24 8 4 2]: [f3, f2*f3, f2*f4, f3*f4, f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
            [4, 10, 11, 12, 17, 21, 23, 24]

[24 8 4 2]: [f3, f2*f3, f2*f4, f3*f4, f1*f2^2, f2^2*f3, f1*f2^2*f3, f2^2*f3*f4]
            [4, 10, 11, 12, 13, 17, 20, 23]

[24 8 4 2]: [f3, f4, f2*f3, f1*f2*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
            [4, 5, 10, 15, 20, 21, 23, 24]

[24 9 4 2]: [f1, f4, f3*f4, f1*f2*f3, f1*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f1*f2^2*f3*f4]
            [2, 5, 12, 14, 16, 20, 21, 22, 24]

[24 10 4 2]: [f1, f2*f3, f2*f4, f1*f2*f3, f1*f3*f4, f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 10, 11, 14, 16, 17, 21, 22, 23, 24]

[24 10 4 2]: [f3, f4, f1*f2, f2*f3, f1*f2*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [4, 5, 6, 10, 15, 18, 19, 21, 23, 24]

[24 10 4 2]: [f1, f1*f2, f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 6, 10, 15, 16, 18, 19, 21, 23, 24]

[24 10 4 3]: [f3, f4, f1*f2, f2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [4, 5, 6, 10, 18, 19, 20, 21, 23, 24]

[24 11 6 4]: [f2, f3, f2^2, f2*f3, f1*f2^2, f1*f2*f3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [3, 4, 9, 10, 13, 14, 20, 21, 22, 23, 24]

[24 11 6 4]: [f2, f2^2, f2*f3, f3*f4, f1*f2^2, f1*f2*f3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [3, 9, 10, 12, 13, 14, 20, 21, 22, 23, 24]

[24 11 6 4]: [f1, f3, f4, f2*f3, f1*f2^2, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 4, 5, 10, 13, 18, 19, 20, 21, 23, 24]

[24 11 6 4]: [f1, f3, f2*f3, f1*f2^2, f1*f3*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 4, 10, 13, 16, 18, 19, 20, 21, 23, 24]

[24 11 6 4]: [f1, f4, f2*f3, f1*f2^2, f1*f3*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2^2*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 5, 10, 13, 16, 18, 19, 20, 21, 23, 24]

[24 11 6 4]: [f1, f4, f1*f2, f2*f3, f1*f2*f3, f1*f2*f4, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^2*f3*f4, f1*f2^2*f3*f4]
             [2, 5, 6, 10, 14, 15, 20, 21, 22, 23, 24]

[24 13 8 6]: [f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f4, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f3, f1*f2*f3*f4]
             [3, 4, 5, 6, 7, 8, 9, 11, 14, 15, 16, 17, 22]

[24 13 8 6]: [f1, f2, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f4, f3*f4, f1*f2^2, f2^2*f3, f2^2*f4, f2*f3*f4]
             [2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 17, 18, 19]

[24 13 12 2]: [f1, f3, 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, 4, 6, 7, 8, 13, 14, 15, 16, 20, 21, 22, 24]

[24 14 8 6]: [f1, f2, f3, f4, f1*f3, f1*f4, f2^2, f2*f4, f1*f2^2, f1*f2*f3, f1*f3*f4, f2^2*f3, f1*f2^2*f3, f1*f2*f3*f4]
             [2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 20, 22]

[24 14 8 7]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f4, f1*f2^2, f1*f2*f3, f1*f3*f4, f2^2*f3, f1*f2*f3*f4]
             [2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 16, 17, 22]

[24 15 10 8]: [f2, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3*f4, f1*f2^2, f1*f2*f4, f2^2*f3, f2^2*f4, f2*f3*f4, f2^2*f3*f4]
              [3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 23]

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

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

[24 15 10 8]: [f1, f2, f3, f1*f2, f1*f3, f1*f4, f2^2, f2*f4, f3*f4, f1*f2*f3, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2*f3*f4]
              [2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 17, 18, 19, 20, 22]

[24 16 12 10]: [f1, f2, f3, f4, f1*f3, f1*f4, f2^2, f2*f4, f3*f4, f1*f2*f3, f1*f2*f4, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2*f3*f4]
               [2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 22]

[24 16 12 10]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2*f3*f4]
               [2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 20, 22]

[24 16 12 10]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2^2*f4, f2*f3*f4, f1*f2^2*f4, f1*f2*f3*f4, f1*f2^2*f3*f4]
               [2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 18, 19, 21, 22, 24]

[24 17 12 10]: [f1, f2, f3, f4, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f1*f2^2, f1*f2*f3, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2*f3*f4, f2^2*f3*f4]
               [2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 17, 18, 19, 20, 22, 23]

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

[24 18 14 12]: [f1, f2, f3, f4, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3*f4, f1*f2^2, f1*f2*f3, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f3, f1*f2*f3*f4, f2^2*f3*f4]
               [2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23]

[24 19 18 14]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f4, f3*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^2*f4, f1*f2*f3*f4, f1*f2^2*f3*f4]
               [2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 24]

[24 20 18 16]: [f1, f2, f3, 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*f3*f4, f2^2*f3*f4]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23]

[24 21 20 18]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3*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*f3*f4, f2^2*f3*f4]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23]