S3xS3 SmallGroup(36, 10)

[36 10 4 2]: [f1, f1*f2, f1*f3, f1*f2*f3, f1*f3^2, f2*f3^2, f2*f3^2*f4, f1*f2*f3^2*f4, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 6, 7, 14, 16, 19, 29, 32, 35, 36]

[36 10 4 2]: [f2, f4, f2*f3, f4^2, f2*f3^2, f1*f3*f4^2, f2*f3^2*f4, f1*f3^2*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [3, 5, 9, 13, 19, 28, 29, 34, 35, 36]

[36 10 4 2]: [f1, f2, f1*f3, f1*f2*f3, f1*f3^2, f2*f3^2, f2*f3^2*f4, f1*f2*f3^2*f4, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 3, 7, 14, 16, 19, 29, 32, 35, 36]

[36 10 4 2]: [f1, f3*f4, f1*f2*f4, f1*f2*f3^2, f2*f3^2*f4, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 12, 15, 24, 29, 31, 32, 33, 35, 36]

[36 10 4 2]: [f1, f1*f2*f4, f1*f4^2, f2*f3^2, f1*f3*f4^2, f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 15, 18, 19, 28, 29, 33, 34, 35, 36]

[36 11 6 2]: [f1, f1*f4, f1*f4^2, f2*f3^2, f1*f2*f4^2, f1*f3*f4^2, f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 8, 18, 19, 26, 28, 29, 33, 34, 35, 36]

[36 11 7 2]: [f3, f4, f3^2, f3*f4, f4^2, f1*f4^2, f2*f3^2, f3^2*f4, f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4^2]
             [4, 5, 11, 12, 13, 18, 19, 22, 23, 31, 36]

[36 13 6 4]: [f3, f4, f1*f2, f3^2, f3*f4, f4^2, f1*f2*f3*f4, f1*f3*f4^2, f2*f3^2*f4, f3^2*f4^2, f1*f3^2*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [4, 5, 6, 11, 12, 13, 25, 28, 29, 31, 34, 35, 36]

[36 13 6 4]: [f1, f4, f2*f4, f3*f4, f4^2, f1*f2*f4, f2*f4^2, f1*f2*f3*f4, f2*f3^2*f4, f3^2*f4^2, f1*f2*f3*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 5, 10, 12, 13, 15, 21, 25, 29, 31, 33, 35, 36]

[36 14 6 4]: [f3, f4, f1*f2, f1*f4, f2*f3, f3^2, f3*f4, f4^2, f1*f3*f4, f2*f3*f4, f1*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4^2]
             [4, 5, 6, 8, 9, 11, 12, 13, 17, 20, 27, 30, 31, 36]

[36 14 6 4]: [f1, f4, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f2*f4^2, f1*f2*f3*f4, f2*f3^2*f4, f3^2*f4^2, f1*f2*f3*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
             [2, 5, 10, 12, 13, 14, 15, 21, 25, 29, 31, 33, 35, 36]

[36 14 6 4]: [f2, f4, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f4^2, f2*f3^2, f2*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f2*f3^2*f4^2]
             [3, 5, 9, 10, 12, 13, 14, 18, 19, 21, 31, 32, 33, 36]

[36 19 18 2]: [f1, f2, f1*f2, f1*f3, f1*f4, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f1*f2*f3^2*f4^2]
              [2, 3, 6, 7, 8, 14, 15, 16, 17, 18, 24, 25, 26, 27, 28, 32, 33, 34, 36]

[36 20 12 10]: [f1, f2, f3, f4, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f4^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f3^2*f4, f2*f3*f4^2]
               [2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 20, 21, 22, 23, 27, 30]

[36 20 12 10]: [f1, f3, f1*f3, f1*f4, f2*f4, f3^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2]
               [2, 4, 7, 8, 10, 11, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 30, 32, 34]

[36 22 14 12]: [f2, f3, f4, f1*f2, f1*f3, f2*f3, f3^2, f4^2, f1*f2*f3, f1*f3^2, f1*f3*f4, f2*f3^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [3, 4, 5, 6, 7, 9, 11, 13, 14, 16, 17, 19, 22, 23, 24, 25, 26, 27, 28, 32, 33, 34]

[36 22 14 12]: [f2, f3, f1*f2, f1*f3, f1*f4, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2]
               [3, 4, 6, 7, 8, 9, 11, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 32, 34]

[36 23 16 14]: [f1, f2, f3, f4, f1*f4, f2*f3, f2*f4, f3^2, f4^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f1*f3^2*f4^2]
               [2, 3, 4, 5, 8, 9, 10, 11, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 34]

[36 24 16 15]: [f1, f2, f3, f4, f1*f2, f1*f3, f2*f3, f2*f4, f3^2, f4^2, f1*f3^2, f1*f4^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f2*f3*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 16, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34]

[36 24 16 15]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f4^2, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f2*f3*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 33]

[36 25 18 16]: [f1, f3, f4, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f3*f4, f4^2, f1*f2*f3, f1*f3^2, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2]
               [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 34]

[36 25 20 16]: [f1, f3, f1*f2, f1*f3, f1*f4, f2*f4, f3^2, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f2*f3^2*f4^2]
               [2, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 36]

[36 25 21 16]: [f1, f3, f4, f1*f2, f1*f3, f1*f4, f3^2, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 19, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34]

[36 25 24 14]: [f2, f3, f1*f2, f1*f3, f2*f3, f2*f4, f3^2, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [3, 4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34]

[36 26 20 18]: [f1, f2, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2]
               [2, 3, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33]

[36 26 20 18]: [f1, f3, f4, f1*f2, f1*f4, f2*f4, f3^2, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34]

[36 26 20 18]: [f2, f4, f1*f2, f1*f3, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f2*f3^2*f4^2]
               [3, 5, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 36]

[36 26 20 18]: [f1, f2, f3, f1*f3, f2*f3, f2*f4, f3^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3^2*f4, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2*f3^2*f4^2]
               [2, 3, 4, 7, 9, 10, 11, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35]

[36 26 20 18]: [f1, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3*f4^2, f1*f3^2*f4^2]
               [2, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34]

[36 26 20 18]: [f1, f2, f3, f4, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f4^2, f1*f2*f4, f1*f3^2, f1*f3*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*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f1*f2*f3^2*f4, f1*f3^2*f4^2]
               [2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34]

[36 31 30 26]: [f1, f2, f3, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f1*f4^2, f2*f3^2, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f1*f2*f3^2*f4^2]
               [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36]

[36 33 32 30]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3^2, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3^2, f1*f3*f4, f2*f3*f4, f2*f4^2, f3^2*f4, f3*f4^2, f1*f2*f3^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3^2*f4, f1*f3*f4^2, f2*f3^2*f4, f2*f3*f4^2, f3^2*f4^2, f1*f2*f3^2*f4, f1*f2*f3*f4^2, f1*f3^2*f4^2, f2*f3^2*f4^2, f1*f2*f3^2*f4^2]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]