(C14xC2):C2 SmallGroup(56, 7)

[56 16 12 2]: [f3, f4, f2*f3, f4^2, f2*f3*f4, f4^3, f2*f3*f4^2, f4^4, f2*f3*f4^3, f4^5, f2*f3*f4^4, f4^6, f2*f3*f4^5, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
              [4, 5, 9, 12, 17, 20, 25, 28, 33, 36, 41, 44, 49, 53, 55, 56]

[56 16 12 2]: [f2, f3, f3*f4, f2*f3*f4, f3*f4^2, f2*f3*f4^2, f3*f4^3, f2*f3*f4^3, f3*f4^4, f2*f3*f4^4, f3*f4^5, f2*f3*f4^5, f3*f4^6, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
              [3, 4, 11, 17, 19, 25, 27, 33, 35, 41, 43, 49, 51, 53, 55, 56]

[56 16 12 2]: [f1, f3, f3*f4, f1*f3*f4, f3*f4^2, f1*f3*f4^2, f3*f4^3, f1*f3*f4^3, f3*f4^4, f1*f3*f4^4, f3*f4^5, f1*f3*f4^5, f3*f4^6, f1*f2*f4^6, f1*f3*f4^6, f1*f2*f3*f4^6]
              [2, 4, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 53, 54, 56]

[56 29 28 2]: [f2, f1*f2, f2*f3, f2*f4, f1*f2*f3, f1*f2*f4, f2*f3*f4, f2*f4^2, f1*f2*f3*f4, f1*f2*f4^2, f2*f3*f4^2, f2*f4^3, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f1*f2*f3*f4^3, f1*f2*f4^4, f2*f3*f4^4, f2*f4^5, f1*f2*f3*f4^4, f1*f2*f4^5, f2*f3*f4^5, f2*f4^6, f1*f2*f3*f4^5, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
              [3, 6, 9, 10, 13, 14, 17, 18, 21, 22, 25, 26, 29, 30, 32, 33, 34, 37, 38, 41, 42, 45, 46, 49, 50, 52, 53, 55, 56]

[56 40 36 26]: [f1, f3, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f4^2, f3*f4^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f4^3, f3*f4^3, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f4^4, f3*f4^4, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f4^5, f3*f4^5, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f3*f4^6]
               [2, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 52, 54]

[56 40 36 26]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f4^6, f1*f2*f3*f4^5, f1*f3*f4^6]
               [2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 50, 52, 54]

[56 40 36 26]: [f2, f3, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f1*f2*f3, f1*f2*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f2*f3*f4^6]
               [3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 52, 55]

[56 43 42 30]: [f1, f2, f3, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f1*f2*f3*f4^5, f1*f2*f4^6, f1*f3*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
               [2, 3, 4, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56]

[56 49 44 42]: [f1, f3, f4, f1*f2, f1*f3, f1*f4, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
               [2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56]

[56 49 48 42]: [f1, f4, f1*f2, f1*f3, f1*f4, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f2*f3*f4^6]
               [2, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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, 55]

[56 50 46 44]: [f1, f2, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
               [2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56]

[56 51 48 46]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f2*f4^6, f2*f3*f4^6, f1*f2*f3*f4^6]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56]

[56 52 50 48]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f3*f4^6, f2*f3*f4^6]
               [2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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, 54, 55]

[56 53 52 50]: [f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f4^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f4^2, f2*f3*f4, f2*f4^2, f3*f4^2, f4^3, f1*f2*f3*f4, f1*f2*f4^2, f1*f3*f4^2, f1*f4^3, f2*f3*f4^2, f2*f4^3, f3*f4^3, f4^4, f1*f2*f3*f4^2, f1*f2*f4^3, f1*f3*f4^3, f1*f4^4, f2*f3*f4^3, f2*f4^4, f3*f4^4, f4^5, f1*f2*f3*f4^3, f1*f2*f4^4, f1*f3*f4^4, f1*f4^5, f2*f3*f4^4, f2*f4^5, f3*f4^5, f4^6, f1*f2*f3*f4^4, f1*f2*f4^5, f1*f3*f4^5, f1*f4^6, f2*f3*f4^5, f2*f4^6, f3*f4^6, f1*f2*f3*f4^5, f1*f3*f4^6, f2*f3*f4^6]
               [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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, 54, 55]