C42 SmallGroup(42, 6)

[42 29 28 16]: [f1, f2, f1*f2, f2^2, f2*f3, f1*f2^2, f1*f2*f3, f2^2*f3, f2*f3^2, f1*f2^2*f3, f1*f2*f3^2, f2^2*f3^2, f2*f3^3, f1*f2^2*f3^2, f1*f2*f3^3, f2^2*f3^3, f2*f3^4, f1*f2^2*f3^3, f1*f2*f3^4, f2^2*f3^4, f2*f3^5, f1*f2^2*f3^4, f1*f2*f3^5, f2^2*f3^5, f2*f3^6, f1*f2^2*f3^5, f1*f2*f3^6, f2^2*f3^6, f1*f2^2*f3^6]
               [2, 3, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42]

[42 37 36 32]: [f1, f3, f1*f3, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f2^2*f3, f2*f3^2, f3^3, f1*f2^2*f3, f1*f2*f3^2, f1*f3^3, f2^2*f3^2, f2*f3^3, f3^4, f1*f2^2*f3^2, f1*f2*f3^3, f1*f3^4, f2^2*f3^3, f2*f3^4, f3^5, f1*f2^2*f3^3, f1*f2*f3^4, f1*f3^5, f2^2*f3^4, f2*f3^5, f3^6, f1*f2^2*f3^4, f1*f2*f3^5, f1*f3^6, f2^2*f3^5, f2*f3^6, f1*f2^2*f3^5, f1*f2*f3^6, f2^2*f3^6, f1*f2^2*f3^6]
               [2, 4, 6, 8, 9, 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]