C22xC2 SmallGroup(44, 4)

[44 12 4 2]: [f2*f3, f3^2, f1*f2*f3, f3^3, f1*f2*f3^2, f2*f3^3, f3^8, f2*f3^8, f3^9, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [7, 8, 9, 12, 13, 15, 32, 35, 36, 41, 43, 44]

[44 12 4 2]: [f2*f3, f1*f2*f3, f3^4, f3^5, f1*f2*f3^4, f2*f3^5, f3^6, f2*f3^6, f3^7, f1*f2*f3^7, f2*f3^10, f1*f2*f3^10]
             [7, 9, 16, 20, 21, 23, 24, 27, 28, 33, 43, 44]

[44 12 4 2]: [f2*f3, f1*f2*f3, f3^3, f3^4, f1*f2*f3^3, f2*f3^4, f3^7, f2*f3^7, f3^8, f1*f2*f3^8, f2*f3^10, f1*f2*f3^10]
             [7, 9, 12, 16, 17, 19, 28, 31, 32, 37, 43, 44]

[44 12 4 2]: [f2*f3, f3^2, f1*f2*f3, f1*f2*f3^2, f1*f3^3, f1*f2*f3^3, f1*f3^8, f3^9, f1*f2*f3^8, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [7, 8, 9, 13, 14, 17, 34, 36, 37, 41, 43, 44]

[44 12 4 2]: [f3, f3^2, f1*f2*f3, f2*f3^2, f3^3, f1*f3^3, f3^8, f1*f3^8, f3^9, f2*f3^9, f3^10, f1*f2*f3^10]
             [4, 8, 9, 11, 12, 14, 32, 34, 36, 39, 40, 44]

[44 12 4 2]: [f2*f3, f1*f2*f3, f1*f3^3, f3^4, f1*f2*f3^3, f1*f2*f3^4, f3^7, f1*f2*f3^7, f1*f3^8, f1*f2*f3^8, f2*f3^10, f1*f2*f3^10]
             [7, 9, 14, 16, 17, 21, 28, 33, 34, 37, 43, 44]

[44 12 4 2]: [f2*f3, f1*f2*f3, f1*f3^2, f3^3, f1*f2*f3^2, f1*f2*f3^3, f3^8, f1*f2*f3^8, f1*f3^9, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [7, 9, 10, 12, 13, 17, 32, 37, 38, 41, 43, 44]

[44 12 4 2]: [f2*f3, f1*f2*f3, f1*f3^2, f1*f2*f3^2, f1*f3^3, f2*f3^3, f1*f3^8, f2*f3^8, f1*f3^9, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [7, 9, 10, 13, 14, 15, 34, 35, 38, 41, 43, 44]

[44 13 9 2]: [f1, f2, f3, f1*f2, f3^2, f3^3, f3^4, f3^5, f3^6, f3^7, f3^8, f3^9, f3^10]
             [2, 3, 4, 5, 8, 12, 16, 20, 24, 28, 32, 36, 40]

[44 23 22 2]: [f1, f2, f1*f2, f1*f3, f2*f3, f1*f3^2, f2*f3^2, f1*f3^3, f2*f3^3, f1*f3^4, f2*f3^4, f1*f3^5, f2*f3^5, f1*f3^6, f2*f3^6, f1*f3^7, f2*f3^7, f1*f3^8, f2*f3^8, f1*f3^9, f2*f3^9, f1*f3^10, f2*f3^10]
              [2, 3, 5, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38, 39, 42, 43]

[44 31 27 20]: [f3, f1*f2, f1*f3, f2*f3, f3^2, f1*f3^2, f2*f3^2, f3^3, f1*f3^3, f2*f3^3, f3^4, f1*f3^4, f2*f3^4, f3^5, f1*f3^5, f2*f3^5, f3^6, f1*f3^6, f2*f3^6, f3^7, f1*f3^7, f2*f3^7, f3^8, f1*f3^8, f2*f3^8, f3^9, f1*f3^9, f2*f3^9, f3^10, f1*f3^10, f2*f3^10]
               [4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43]

[44 41 40 38]: [f1, f3, f1*f3, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f2*f3^2, f3^3, f1*f2*f3^2, f1*f3^3, f2*f3^3, f3^4, f1*f2*f3^3, f1*f3^4, f2*f3^4, f3^5, f1*f2*f3^4, f1*f3^5, f2*f3^5, f3^6, f1*f2*f3^5, f1*f3^6, f2*f3^6, f3^7, f1*f2*f3^6, f1*f3^7, f2*f3^7, f3^8, f1*f2*f3^7, f1*f3^8, f2*f3^8, f3^9, f1*f2*f3^8, f1*f3^9, f2*f3^9, f3^10, f1*f2*f3^9, f1*f3^10, f2*f3^10, f1*f2*f3^10]
               [2, 4, 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]