C2x((C3xC3):C3) SmallGroup(54, 10)

[54 21 12 4]: [f1, f2*f3, f2*f4, f3*f4, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f2^2*f3^2, f2^2*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f2^2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
              [2, 10, 11, 13, 21, 22, 23, 24, 25, 26, 27, 35, 37, 39, 40, 45, 47, 48, 49, 53, 54]

[54 21 12 4]: [f1, f2, f3, f4, f1*f4, f2^2, f2*f3, f3^2, f4^2, f1*f4^2, f2^2*f3, f2^2*f4, f2*f3^2, f2*f4^2, f3^2*f4, f3*f4^2, f2*f3*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f2^2*f3^2*f4^2]
              [2, 3, 4, 5, 8, 9, 10, 12, 14, 20, 21, 22, 23, 25, 26, 27, 39, 47, 48, 49, 53]

[54 24 12 9]: [f4, f1*f2, f1*f3, f4^2, f1*f2^2, f1*f2*f3, f1*f3^2, f2^2*f3, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2*f3^2, f2^2*f3^2, f2*f3*f4^2, f1*f2*f3*f4^2, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f2^2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
              [5, 6, 7, 14, 15, 16, 18, 21, 23, 24, 26, 27, 28, 30, 35, 39, 45, 48, 49, 50, 51, 52, 53, 54]

[54 24 12 9]: [f2, f3, f1*f4, f2^2, f3^2, f1*f2*f3, f1*f3*f4, f1*f4^2, f2^2*f3, f2*f3^2, f2*f3*f4, f1*f2^2*f3, f1*f2*f3^2, f2^2*f3^2, f2*f3*f4^2, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f2^2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
              [3, 4, 8, 9, 12, 16, 19, 20, 21, 23, 24, 28, 30, 35, 39, 45, 46, 48, 49, 50, 51, 52, 53, 54]

[54 27 15 12]: [f1, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f3^2, f4^2, f1*f2^2, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2^2*f3, f2*f3^2, f2*f3*f4, f1*f2*f3*f4, f2^2*f3^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2]
               [2, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 18, 19, 20, 21, 23, 24, 31, 35, 41, 42, 43, 44, 46, 47, 48, 49]

[54 27 15 12]: [f1, f1*f2, f1*f3, f2*f3, f1*f2^2, f1*f2*f4, f1*f3^2, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2^2*f4, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2]
               [2, 6, 7, 10, 15, 17, 18, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 41, 42, 43, 44, 47, 48, 49]

[54 33 24 16]: [f1, f2, f3, f2^2, f2*f3, f2*f4, f3^2, f3*f4, f1*f2*f4, f1*f3*f4, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3*f4, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f2^2*f3^2*f4^2]
               [2, 3, 4, 9, 10, 11, 12, 13, 17, 19, 21, 22, 23, 24, 25, 26, 27, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 53]

[54 33 24 16]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3^2, f3*f4, f4^2, f1*f2^2, f1*f3^2, f1*f4^2, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f3^2*f4^2, f1*f2^2*f3*f4, f1*f2*f3^2*f4, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 20, 21, 22, 23, 24, 25, 26, 27, 35, 36, 37, 38, 40, 42, 44, 47, 48, 49]

[54 37 36 20]: [f1, f2, f3, f1*f2, f1*f3, f2^2, f2*f4, f3^2, f3*f4, f1*f2^2, f1*f2*f4, f1*f3^2, f1*f3*f4, f2^2*f3, f2^2*f4, f2*f3^2, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f3^2*f4^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2]
               [2, 3, 4, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 42, 43, 44, 46, 48, 49, 51, 52]

[54 42 33 32]: [f2, f3, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3^2, f3*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f4^2, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f2^2*f3^2*f4^2]
               [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 53]

[54 42 33 32]: [f2, f3, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f2*f3*f4^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f2^2*f3^2*f4^2]
               [3, 4, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53]

[54 42 33 32]: [f2, f3, f4, f1*f2, f1*f3, f2^2, f2*f3, f2*f4, f3^2, f4^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
               [3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54]

[54 42 33 32]: [f2, f3, f4, f1*f2, f1*f3, f2^2, f2*f3, f2*f4, f3^2, f3*f4, f4^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f2^2*f3, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f2^2*f3^2*f4^2]
               [3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 53]

[54 45 39 36]: [f1, f2, f3, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
               [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54]

[54 45 39 36]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2^2, f2*f3, f2*f4, f3^2, f4^2, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54]

[54 49 48 44]: [f1, f2, f3, f1*f2, f1*f3, f2^2, f2*f3, f2*f4, f3^2, f3*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2^2*f3, f2^2*f4, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2^2*f3^2, f2^2*f3*f4, f2^2*f4^2, f2*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2^2*f3^2, f1*f2^2*f3*f4, f1*f2^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2^2*f3^2*f4, f2^2*f3*f4^2, f2*f3^2*f4^2, f1*f2^2*f3^2*f4, f1*f2^2*f3*f4^2, f1*f2*f3^2*f4^2, f2^2*f3^2*f4^2, f1*f2^2*f3^2*f4^2]
               [2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54]