C56 SmallGroup(56, 2)

[56 29 28 2]: [f1, f4, f1*f2, f1*f3, f1*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f1*f3*f4, f1*f2^3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f1*f2^4, f1*f2^3*f3, f1*f2^3*f4, f1*f2^2*f3*f4, f1*f2^5, f1*f2^4*f3, f1*f2^4*f4, f1*f2^3*f3*f4, f1*f2^6, f1*f2^5*f3, f1*f2^5*f4, f1*f2^4*f3*f4, f1*f2^6*f3, f1*f2^6*f4, f1*f2^5*f3*f4, f1*f2^6*f3*f4]
              [2, 5, 6, 7, 8, 13, 14, 15, 16, 21, 22, 23, 24, 29, 30, 31, 32, 37, 38, 39, 40, 45, 46, 47, 48, 52, 53, 54, 56]

[56 43 42 30]: [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*f2^3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^3*f3, f2^2*f3*f4, f1*f2^4, f1*f2^3*f3, f1*f2^3*f4, f1*f2^2*f3*f4, f2^4*f3, f2^3*f3*f4, f1*f2^5, f1*f2^4*f3, f1*f2^4*f4, f1*f2^3*f3*f4, f2^5*f3, f2^4*f3*f4, f1*f2^6, f1*f2^5*f3, f1*f2^5*f4, f1*f2^4*f3*f4, f2^6*f3, f2^5*f3*f4, f1*f2^6*f3, f1*f2^6*f4, f1*f2^5*f3*f4, f2^6*f3*f4, f1*f2^6*f3*f4]
               [2, 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, 49, 51, 52, 53, 54, 55, 56]

[56 49 48 42]: [f2, f4, f1*f2, f2^2, f2*f3, f2*f4, f1*f2^2, f1*f2*f3, f1*f2*f4, f2^3, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^4, f2^3*f3, f2^3*f4, f2^2*f3*f4, f1*f2^4, f1*f2^3*f3, f1*f2^3*f4, f1*f2^2*f3*f4, f2^5, f2^4*f3, f2^4*f4, f2^3*f3*f4, f1*f2^5, f1*f2^4*f3, f1*f2^4*f4, f1*f2^3*f3*f4, f2^6, f2^5*f3, f2^5*f4, f2^4*f3*f4, f1*f2^6, f1*f2^5*f3, f1*f2^5*f4, f1*f2^4*f3*f4, f2^6*f3, f2^6*f4, f2^5*f3*f4, f1*f2^6*f3, f1*f2^6*f4, f1*f2^5*f3*f4, f2^6*f3*f4, f1*f2^6*f3*f4]
               [3, 5, 6, 9, 10, 11, 13, 14, 15, 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, 53, 54, 55, 56]

[56 53 52 50]: [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, f2^3, f2^2*f3, f2^2*f4, f2*f3*f4, f1*f2^3, f1*f2^2*f3, f1*f2^2*f4, f1*f2*f3*f4, f2^4, f2^3*f3, f2^3*f4, f2^2*f3*f4, f1*f2^4, f1*f2^3*f3, f1*f2^3*f4, f1*f2^2*f3*f4, f2^5, f2^4*f3, f2^4*f4, f2^3*f3*f4, f1*f2^5, f1*f2^4*f3, f1*f2^4*f4, f1*f2^3*f3*f4, f2^6, f2^5*f3, f2^5*f4, f2^4*f3*f4, f1*f2^6, f1*f2^5*f3, f1*f2^5*f4, f1*f2^4*f3*f4, f2^6*f3, f2^6*f4, f2^5*f3*f4, f1*f2^6*f3, f1*f2^6*f4, f1*f2^5*f3*f4, f2^6*f3*f4, f1*f2^6*f3*f4]
               [2, 3, 5, 6, 7, 8, 9, 10, 11, 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, 53, 54, 55, 56]