Tommy Hofmann

Normal CM-fields with relative class number one

This is a list of normal CM-fields with relative class number one as published in the preprint "Normal CM-fields with class number one". Under the assumption of the generalized Riemann Hypothesis, these are all normal CM-fields with relative class number one. For each field \(L\), we list the Galois group \(\operatorname{Gal}(L/\mathbf Q)\), the identifyer "id" of the Galois group in the small group library, a defining polynomial \(f\), the class number \(h_L\) and the discriminant \(\operatorname{disc}(L)\) in factored form.

The list of fields is also accessible as a text file, containing the defining polynomials as list of coefficients: poly.txt. Thus an entry of the form [a_0,a_1,...,a_d] corresponds to the polynomial \(a_d x^d + \dotsb + a_1 x + a_0\).

\(\operatorname{Gal}(L/\mathbf Q)\)id\(f\)\(h_L\)\(\operatorname{disc}(L)\)
\(\mathrm C_2\)2,1\(x^{2} - x + 1\)\(1\)\(-3\)
\(\mathrm C_2\)2,1\(x^{2} + 1\)\(1\)\(-2^{2}\)
\(\mathrm C_2\)2,1\(x^{2} - x + 2\)\(1\)\(-7\)
\(\mathrm C_2\)2,1\(x^{2} + 2\)\(1\)\(-2^{3}\)
\(\mathrm C_2\)2,1\(x^{2} - x + 3\)\(1\)\(-11\)
\(\mathrm C_2\)2,1\(x^{2} - x + 5\)\(1\)\(-19\)
\(\mathrm C_2\)2,1\(x^{2} - x + 11\)\(1\)\(-43\)
\(\mathrm C_2\)2,1\(x^{2} - x + 17\)\(1\)\(-67\)
\(\mathrm C_2\)2,1\(x^{2} - x + 41\)\(1\)\(-163\)
\(\mathrm C_4\)4,1\(x^{4} - x^{3} + x^{2} - x + 1\)\(1\)\(5^{3}\)
\(\mathrm C_4\)4,1\(x^{4} + 4x^{2} + 2\)\(1\)\(2^{11}\)
\(\mathrm C_4\)4,1\(x^{4} - x^{3} + 2x^{2} + 4x + 3\)\(1\)\(13^{3}\)
\(\mathrm C_4\)4,1\(x^{4} - x^{3} + 4x^{2} - 20x + 23\)\(1\)\(29^{3}\)
\(\mathrm C_4\)4,1\(x^{4} - x^{3} + 5x^{2} - 7x + 49\)\(1\)\(37^{3}\)
\(\mathrm C_4\)4,1\(x^{4} + x^{3} + 7x^{2} - 43x + 47\)\(1\)\(53^{3}\)
\(\mathrm C_4\)4,1\(x^{4} + x^{3} + 8x^{2} + 42x + 117\)\(1\)\(61^{3}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{2} + 1\)\(1\)\(2^{4} 3^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} + 2x^{2} + x + 1\)\(1\)\(3^{2} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 1\)\(1\)\(2^{8}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 3x^{2} + 1\)\(1\)\(2^{4} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - x^{2} - 2x + 4\)\(1\)\(3^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 2x^{2} + 4\)\(1\)\(2^{6} 3^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{2} + 4\)\(1\)\(2^{6} 3^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 3x^{2} + 4\)\(1\)\(2^{4} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 2x^{2} - 3x + 9\)\(1\)\(3^{2} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + x^{2} + 9\)\(1\)\(5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 6x^{2} + 4\)\(1\)\(2^{6} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 5x^{2} + 9\)\(1\)\(2^{4} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} + 5x^{2} + 4x + 16\)\(1\)\(3^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 7x^{2} + 9\)\(1\)\(2^{4} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 9x^{2} - 8x + 2\)\(1\)\(2^{6} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 4x^{2} - 5x + 25\)\(1\)\(3^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 7x^{2} + 16\)\(2\)\(2^{4} 3^{2} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 28x^{2} - 29x + 841\)\(2\)\(3^{2} 5^{2} 23^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 29x^{2} + 121\)\(2\)\(3^{2} 7^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 45x^{2} + 529\)\(2\)\(2^{4} 7^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 31x^{2} - 30x + 134\)\(2\)\(2^{4} 7^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 27x^{2} + 289\)\(1\)\(7^{2} 61^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 23x^{2} - 22x + 7\)\(2\)\(2^{6} 3^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 57x^{2} + 841\)\(2\)\(2^{4} 5^{2} 23^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 841\)\(2\)\(2^{8} 29^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 37x^{2} + 225\)\(3\)\(7^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 27x^{2} + 64\)\(3\)\(11^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 40x^{2} - 41x + 1681\)\(1\)\(3^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 39x^{2} - 38x + 227\)\(1\)\(2^{6} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 46x^{2} - 47x + 2209\)\(2\)\(3^{2} 11^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 31x^{2} + 100\)\(2\)\(3^{2} 11^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 33x^{2} - 32x + 113\)\(2\)\(2^{4} 11^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 36x^{2} + 361\)\(2\)\(2^{8} 37^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 29x^{2} + 49\)\(2\)\(3^{2} 5^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 81x^{2} + 1681\)\(1\)\(2^{4} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 58x^{2} + 3364\)\(2\)\(2^{6} 3^{2} 29^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 58x^{2} - 59x + 3481\)\(2\)\(3^{2} 5^{2} 47^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 51x^{2} - 50x + 443\)\(2\)\(2^{6} 7^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 39x^{2} + 196\)\(1\)\(11^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 61x^{2} + 729\)\(2\)\(5^{2} 7^{2} 23^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 31x^{2} + 36\)\(5\)\(19^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 33x^{2} - 32x + 41\)\(2\)\(2^{4} 5^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 65x^{2} + 841\)\(2\)\(3^{2} 7^{2} 41^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 63x^{2} - 62x + 731\)\(2\)\(2^{6} 5^{2} 23^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 117x^{2} + 3481\)\(6\)\(2^{4} 5^{2} 47^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 37x^{2} - 36x + 77\)\(2\)\(2^{4} 13^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 51x^{2} + 400\)\(2\)\(7^{2} 11^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 41x^{2} + 169\)\(2\)\(3^{2} 5^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 35x^{2} - 34x + 31\)\(2\)\(2^{6} 3^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 85x^{2} + 1521\)\(1\)\(7^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 219x^{2} + 10816\)\(2\)\(7^{2} 11^{2} 61^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 79x^{2} + 324\)\(2\)\(5^{2} 23^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 143x^{2} + 3844\)\(6\)\(3^{2} 19^{2} 89^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 99x^{2} + 1024\)\(2\)\(5^{2} 7^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 79x^{2} - 78x + 47\)\(2\)\(2^{6} 11^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 79x^{2} + 36\)\(14\)\(7^{2} 13^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 97x^{2} - 96x + 713\)\(2\)\(2^{4} 37^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 103x^{2} - 102x + 971\)\(2\)\(2^{6} 5^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 103x^{2} + 900\)\(1\)\(43^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 211x^{2} + 9216\)\(2\)\(13^{2} 19^{2} 31^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 91x^{2} + 144\)\(10\)\(5^{2} 23^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 95x^{2} + 196\)\(2\)\(3^{2} 41^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 107x^{2} + 784\)\(2\)\(3^{2} 17^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 109x^{2} - 108x + 797\)\(2\)\(2^{4} 13^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 139x^{2} - 138x + 2267\)\(2\)\(2^{6} 29^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 139x^{2} + 2304\)\(2\)\(5^{2} 43^{2} 47^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 115x^{2} + 576\)\(1\)\(67^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 155x^{2} + 3136\)\(2\)\(3^{2} 43^{2} 89^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 127x^{2} - 126x + 383\)\(2\)\(2^{6} 11^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 127x^{2} + 324\)\(2\)\(7^{2} 13^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 151x^{2} + 1764\)\(2\)\(5^{2} 47^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 235x^{2} + 9216\)\(2\)\(7^{2} 43^{2} 61^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 139x^{2} + 144\)\(2\)\(5^{2} 23^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 157x^{2} - 156x + 53\)\(2\)\(2^{4} 37^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 235x^{2} + 7056\)\(2\)\(13^{2} 31^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 247x^{2} + 8100\)\(14\)\(7^{2} 61^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 175x^{2} + 36\)\(2\)\(11^{2} 17^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 199x^{2} - 198x + 347\)\(2\)\(2^{6} 29^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 5x^{2} + 25\)\(2\)\(2^{4} 3^{2} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 9x^{2} + 25\)\(1\)\(2^{4} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 9x^{2} + 1\)\(1\)\(7^{2} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 4x^{2} + 9\)\(2\)\(2^{8} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 25\)\(2\)\(2^{8} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 11x^{2} - 10x + 3\)\(1\)\(2^{6} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 3x^{2} - 2x + 23\)\(1\)\(2^{6} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 3x^{2} + 25\)\(1\)\(7^{2} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 8x^{2} - 9x + 81\)\(2\)\(3^{2} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 11x^{2} + 4\)\(2\)\(3^{2} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 10x^{2} + 100\)\(2\)\(2^{6} 3^{2} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 13x^{2} - 12x + 6\)\(2\)\(2^{6} 3^{2} 5^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} + 11x^{2} + 10x + 100\)\(1\)\(3^{2} 41^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 10x^{2} - 11x + 121\)\(1\)\(3^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 13x^{2} + 9\)\(1\)\(7^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 17x^{2} + 81\)\(2\)\(2^{4} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 15x^{2} - 14x + 14\)\(2\)\(2^{4} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 19x^{2} + 81\)\(1\)\(2^{4} 37^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 15x^{2} - 14x + 11\)\(1\)\(2^{6} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 21x^{2} + 121\)\(1\)\(2^{4} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 3x^{2} + 49\)\(1\)\(11^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} - 16x^{2} - 17x + 289\)\(1\)\(3^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 12x^{2} + 49\)\(2\)\(2^{8} 13^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 15x^{2} + 4\)\(1\)\(11^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} - 9x^{2} + 10x + 83\)\(1\)\(2^{6} 29^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 22x^{2} + 484\)\(2\)\(2^{6} 3^{2} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 19x^{2} - 18x + 15\)\(2\)\(2^{6} 3^{2} 11^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - x^{3} + 23x^{2} + 22x + 484\)\(1\)\(3^{2} 89^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 33x^{2} + 289\)\(1\)\(2^{4} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 25x^{2} - 24x + 74\)\(2\)\(2^{6} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 23x^{2} - 22x + 51\)\(2\)\(2^{6} 5^{2} 7^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 25x^{2} + 81\)\(1\)\(7^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 27x^{2} - 26x + 83\)\(1\)\(2^{6} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 43x^{2} + 144\)\(1\)\(19^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 87x^{2} - 86x + 1523\)\(3\)\(2^{6} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 97x^{2} + 2025\)\(2\)\(7^{2} 11^{2} 17^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 45x^{2} - 44x + 149\)\(2\)\(2^{4} 5^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 67x^{2} + 784\)\(2\)\(3^{2} 11^{2} 41^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 39x^{2} + 4\)\(2\)\(5^{2} 7^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 47x^{2} - 46x + 127\)\(2\)\(2^{6} 3^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 201x^{2} + 10201\)\(2\)\(2^{4} 13^{2} 31^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 121x^{2} + 3249\)\(2\)\(5^{2} 7^{2} 47^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 55x^{2} - 54x + 311\)\(2\)\(2^{6} 11^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 213x^{2} + 11449\)\(6\)\(2^{4} 7^{2} 61^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 43x^{2} - 42x + 11\)\(2\)\(2^{6} 5^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 55x^{2} + 324\)\(2\)\(7^{2} 13^{2} 19^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 87x^{2} + 1444\)\(1\)\(11^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 137x^{2} + 4225\)\(2\)\(3^{2} 7^{2} 89^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 123x^{2} - 122x + 3251\)\(2\)\(2^{6} 5^{2} 47^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 71x^{2} + 676\)\(2\)\(3^{2} 19^{2} 41^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 51x^{2} + 64\)\(2\)\(5^{2} 7^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 89x^{2} + 1369\)\(2\)\(3^{2} 5^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 123x^{2} - 122x + 3083\)\(2\)\(2^{6} 11^{2} 29^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 55x^{2} - 54x + 59\)\(2\)\(2^{6} 5^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 85x^{2} - 84x + 1061\)\(2\)\(2^{4} 19^{2} 37^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 205x^{2} + 9801\)\(2\)\(7^{2} 13^{2} 31^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 55x^{2} + 36\)\(1\)\(43^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 91x^{2} + 1296\)\(1\)\(19^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 207x^{2} - 206x + 9803\)\(2\)\(2^{6} 13^{2} 31^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 93x^{2} - 92x + 1301\)\(2\)\(2^{4} 5^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 219x^{2} - 218x + 11027\)\(2\)\(2^{6} 7^{2} 61^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 61x^{2} - 60x + 29\)\(2\)\(2^{4} 13^{2} 67^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 67x^{2} - 66x + 143\)\(2\)\(2^{6} 11^{2} 43^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 95x^{2} - 94x + 1231\)\(2\)\(2^{6} 3^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} - 2x^{3} + 127x^{2} - 126x + 2867\)\(2\)\(2^{6} 19^{2} 29^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 207x^{2} + 9604\)\(2\)\(11^{2} 13^{2} 31^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 199x^{2} + 324\)\(2\)\(5^{2} 47^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 215x^{2} + 676\)\(2\)\(3^{2} 89^{2} 163^{2}\)
\(\mathrm C_2^2\)4,2\(x^{4} + 283x^{2} + 3600\)\(2\)\(13^{2} 31^{2} 163^{2}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\)\(1\)\(-7^{5}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{3} + 1\)\(1\)\(-3^{9}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1\)\(1\)\(-3^{3} 7^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 5x^{4} + 6x^{2} + 1\)\(1\)\(-2^{6} 7^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 6x^{4} + 9x^{2} + 1\)\(1\)\(-2^{6} 3^{8}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 5x^{4} - 6x^{3} + 15x^{2} - 4x + 1\)\(1\)\(-3^{3} 13^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 10x^{4} + 24x^{2} + 8\)\(1\)\(-2^{9} 7^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - 3x^{5} + 3x^{4} - 3x^{3} + 21x^{2} - 3x + 37\)\(1\)\(-3^{8} 7^{3}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 2x^{4} - 8x^{3} - x^{2} + 5x + 7\)\(1\)\(-19^{5}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{5} + 4x^{4} - 3x^{3} + 29x^{2} - 4x + 71\)\(1\)\(-7^{4} 11^{3}\)
\(\mathrm C_6\)6,2\(x^{6} + 13x^{4} + 50x^{2} + 49\)\(1\)\(-2^{6} 19^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} - 3x^{4} - 7x^{3} + 25x^{2} + 55x + 79\)\(1\)\(-7^{3} 13^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - 2x^{5} - x^{4} - 2x^{3} + 34x^{2} + 28x + 73\)\(1\)\(-2^{9} 13^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 11x^{4} + 6x^{3} + 108x^{2} + 80x + 64\)\(1\)\(-3^{3} 31^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 35x^{3} + 343\)\(3\)\(-3^{9} 7^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 28x^{3} + 343\)\(3\)\(-3^{9} 7^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{5} + 15x^{4} + 30x^{3} + 188x^{2} + 112x + 64\)\(1\)\(-3^{3} 43^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - 14x^{3} + 63x^{2} + 168x + 161\)\(3\)\(-3^{8} 7^{5}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 4x^{4} - 23x^{3} + 67x^{2} - 50x + 44\)\(1\)\(-43^{5}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + x^{4} - 13x^{3} + 71x^{2} - 419x + 827\)\(3\)\(-7^{5} 13^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - 26x^{3} + 2197\)\(3\)\(-3^{9} 13^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 6x^{4} + 46x^{3} + 123x^{2} + 169x + 617\)\(1\)\(-67^{5}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{5} + x^{4} - 99x^{3} + 281x^{2} + 573x + 981\)\(3\)\(-7^{5} 19^{4}\)
\(\mathrm C_6\)6,2\(x^{6} - x^{5} + x^{4} - 113x^{3} + 1037x^{2} - 5125x + 8975\)\(3\)\(-7^{5} 31^{4}\)
\(\mathrm C_6\)6,2\(x^{6} + 76x^{3} + 684x^{2} + 2508x + 3743\)\(3\)\(-3^{8} 19^{5}\)
\(\mathrm C_6\)6,2\(x^{6} + x^{5} + 2x^{4} - 255x^{3} + 1291x^{2} + 784x + 2192\)\(3\)\(-13^{4} 19^{5}\)
\(\mathrm C_8\)8,1\(x^{8} + 8x^{6} + 20x^{4} + 16x^{2} + 2\)\(1\)\(2^{31}\)
\(\mathrm C_8\)8,1\(x^{8} + x^{7} + 3x^{6} + 11x^{5} + 44x^{4} - 53x^{3} + 153x^{2} - 160x + 59\)\(1\)\(41^{7}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\)\(1\)\(3^{4} 5^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - x^{6} + x^{4} - x^{2} + 1\)\(1\)\(2^{8} 5^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 1\)\(1\)\(2^{24}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16\)\(1\)\(5^{6} 7^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16\)\(1\)\(2^{12} 5^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16\)\(1\)\(2^{12} 5^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 4x^{6} + 14x^{4} + 8x^{2} + 4\)\(1\)\(2^{22} 3^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4\)\(1\)\(2^{22} 3^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + x^{7} + 4x^{6} + 7x^{5} + 19x^{4} - 21x^{3} + 36x^{2} - 27x + 81\)\(1\)\(5^{6} 13^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 3x^{6} + 18x^{4} + 4x^{2} + 9\)\(1\)\(2^{8} 13^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + x^{7} + 5x^{6} + 9x^{5} + 29x^{4} - 36x^{3} + 80x^{2} - 64x + 256\)\(1\)\(5^{6} 17^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 12x^{6} + 30x^{4} + 24x^{2} + 4\)\(1\)\(2^{22} 5^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{7} - 8x^{5} + 27x^{4} - 62x^{3} + 117x^{2} - 23x + 29\)\(1\)\(5^{4} 13^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 49\)\(2\)\(2^{24} 5^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 625\)\(2\)\(2^{24} 5^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{7} + 12x^{6} - 26x^{5} + 57x^{4} - 26x^{3} - 27x^{2} + 37x + 53\)\(1\)\(7^{4} 13^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{7} - 3x^{6} + 16x^{5} + 12x^{4} + 34x^{3} + 48x^{2} - 140x + 113\)\(1\)\(2^{12} 13^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 4x^{7} + 26x^{6} - 64x^{5} + 163x^{4} - 224x^{3} + 210x^{2} - 108x + 23\)\(1\)\(2^{22} 11^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 9x^{6} + 109x^{4} - 441x^{2} + 2401\)\(1\)\(2^{8} 37^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{7} + 17x^{6} - 60x^{5} + 148x^{4} - 102x^{3} + 108x^{2} - 532x + 1009\)\(1\)\(2^{12} 29^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + x^{7} - 27x^{6} + 30x^{5} + 546x^{4} - 506x^{3} - 6691x^{2} - 239x + 57121\)\(2\)\(3^{4} 7^{4} 17^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 4x^{7} + 42x^{6} - 112x^{5} + 427x^{4} - 672x^{3} + 1002x^{2} - 684x + 207\)\(2\)\(2^{22} 3^{4} 11^{4}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} - 2x^{7} + 24x^{6} + 42x^{5} + 243x^{4} + 38x^{3} + 889x^{2} + 8007x + 9837\)\(5\)\(7^{4} 61^{6}\)
\(\mathrm C_2\times \mathrm C_4\)8,2\(x^{8} + 2x^{7} + 68x^{6} + 130x^{5} + 1542x^{4} + 2140x^{3} + 10489x^{2} + 13692x + 33188\)\(2\)\(7^{4} 11^{4} 17^{6}\)
\(\mathrm D_4\)8,3\(x^{8} - 2x^{7} + 3x^{6} + 20x^{5} + 3x^{4} - 2x^{3} + 9x^{2} - 8x + 8\)\(1\)\(2^{12} 17^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 15x^{6} + 48x^{4} + 15x^{2} + 1\)\(1\)\(5^{4} 41^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + x^{6} + 4x^{5} - 38x^{4} + 2x^{3} + 123x^{2} + 34x + 17\)\(1\)\(13^{4} 17^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 2x^{7} + 18x^{6} + 34x^{5} + 83x^{4} + 62x^{3} - 19x^{2} - 15x + 5\)\(1\)\(5^{4} 61^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 2x^{7} + 18x^{6} - 4x^{5} - 3x^{4} + 50x^{3} - 21x^{2} - 43x + 23\)\(1\)\(13^{4} 29^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 25x^{6} + 137x^{4} + 100x^{2} + 16\)\(1\)\(5^{4} 109^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 4x^{7} + 34x^{6} + 88x^{5} + 305x^{4} + 468x^{3} + 556x^{2} + 336x + 71\)\(1\)\(2^{12} 73^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 26x^{6} + 28x^{5} + 99x^{4} + 8x^{3} - 2x^{2} + 88x + 68\)\(1\)\(2^{12} 89^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 2x^{7} + 28x^{6} + 54x^{5} + 187x^{4} + 156x^{3} - 25x^{2} - 21x + 19\)\(1\)\(5^{4} 149^{4}\)
\(\mathrm D_4\)8,3\(x^{8} - 2x^{7} + 38x^{6} - 74x^{5} + 337x^{4} - 306x^{3} + 65x^{2} - 59x + 89\)\(3\)\(5^{4} 269^{4}\)
\(\mathrm D_4\)8,3\(x^{8} - 2x^{7} + 21x^{6} + 10x^{5} + 250x^{4} + 120x^{3} + 488x^{2} + 5774x + 6563\)\(1\)\(29^{4} 53^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 42x^{6} - 44x^{5} + 235x^{4} + 8x^{3} - 114x^{2} - 128x + 124\)\(1\)\(2^{12} 233^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 45x^{6} + 417x^{4} + 180x^{2} + 16\)\(1\)\(5^{4} 389^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 2x^{7} + 44x^{6} - 4x^{5} + 87x^{4} + 192x^{3} - 127x^{2} - 195x + 117\)\(1\)\(13^{4} 157^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 8x^{7} + 54x^{6} + 212x^{5} + 709x^{4} + 1572x^{3} + 704x^{2} - 1256x + 668\)\(1\)\(2^{12} 281^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 51x^{6} + 648x^{4} + 816x^{2} + 256\)\(1\)\(17^{4} 137^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 16x^{6} + 194x^{4} - 1313x^{2} + 4225\)\(1\)\(13^{4} 181^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 2x^{7} + 68x^{6} - 6x^{5} + 558x^{4} + 340x^{3} + 713x^{2} - 2276x + 1828\)\(3\)\(17^{4} 257^{4}\)
\(\mathrm D_4\)8,3\(x^{8} + 7x^{6} + 48x^{5} - 1040x^{4} + 168x^{3} + 17251x^{2} + 17232x + 100557\)\(1\)\(73^{4} 97^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - x^{4} + 1\)\(1\)\(2^{16} 3^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1\)\(1\)\(2^{8} 3^{4} 5^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 7x^{4} + 1\)\(1\)\(2^{16} 5^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16\)\(1\)\(2^{8} 3^{4} 7^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - x^{7} - 4x^{6} - 9x^{5} + 23x^{4} + 18x^{3} - 16x^{2} + 8x + 16\)\(1\)\(3^{4} 5^{4} 7^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 6x^{6} + 32x^{4} - 24x^{2} + 16\)\(1\)\(2^{12} 3^{4} 5^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81\)\(1\)\(2^{8} 3^{4} 11^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 9x^{6} + 37x^{4} - 36x^{2} + 16\)\(1\)\(2^{8} 5^{4} 7^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 2x^{7} + 7x^{6} - 14x^{5} + 39x^{4} - 4x^{3} - 44x^{2} + 80x + 100\)\(1\)\(2^{12} 3^{4} 7^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 7x^{4} + 81\)\(1\)\(2^{16} 11^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625\)\(1\)\(2^{8} 3^{4} 19^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 4x^{7} + 22x^{6} - 52x^{5} + 129x^{4} - 176x^{3} + 76x^{2} + 4x + 31\)\(1\)\(2^{12} 3^{4} 11^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 4x^{7} + 26x^{6} - 64x^{5} + 159x^{4} - 216x^{3} + 218x^{2} - 120x + 36\)\(1\)\(2^{12} 5^{4} 7^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 4x^{7} + 28x^{6} - 70x^{5} + 193x^{4} - 274x^{3} + 272x^{2} - 146x + 29\)\(1\)\(2^{8} 7^{4} 13^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} - 4x^{7} - 4x^{6} + 26x^{5} + 81x^{4} - 210x^{3} - 448x^{2} + 558x + 1773\)\(1\)\(2^{8} 7^{4} 19^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 2x^{7} - 20x^{6} - 40x^{5} + 120x^{4} + 88x^{3} + 139x^{2} + 358x + 268\)\(1\)\(3^{4} 11^{4} 17^{4}\)
\(\mathrm C_2^3\)8,5\(x^{8} + 2x^{7} + 4x^{6} - 10x^{5} + 72x^{4} + 220x^{3} - 539x^{2} - 146x + 1996\)\(1\)\(3^{4} 11^{4} 19^{4}\)
\(\mathrm C_{10}\)10,2\(x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\)\(1\)\(-11^{9}\)
\(\mathrm C_{10}\)10,2\(x^{10} - x^{9} + 5x^{8} - 2x^{7} + 16x^{6} - 7x^{5} + 20x^{4} + x^{3} + 12x^{2} - 3x + 1\)\(1\)\(-3^{5} 11^{8}\)
\(\mathrm C_{10}\)10,2\(x^{10} + 9x^{8} + 28x^{6} + 35x^{4} + 15x^{2} + 1\)\(1\)\(-2^{10} 11^{8}\)
\(\mathrm C_{12}\)12,2\(x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\)\(1\)\(13^{11}\)
\(\mathrm C_{12}\)12,2\(x^{12} - x^{11} + 3x^{10} - 4x^{9} + 9x^{8} + 2x^{7} + 12x^{6} + x^{5} + 25x^{4} - 11x^{3} + 5x^{2} - 2x + 1\)\(1\)\(5^{9} 7^{8}\)
\(\mathrm C_{12}\)12,2\(x^{12} + 3x^{10} - x^{9} + 9x^{8} + 9x^{7} + 28x^{6} + 18x^{5} + 75x^{4} + 26x^{3} + 9x^{2} + 3x + 1\)\(1\)\(3^{16} 5^{9}\)
\(\mathrm C_{12}\)12,2\(x^{12} + x^{11} + 2x^{10} - 20x^{9} - 13x^{8} - 19x^{7} + 85x^{6} + 51x^{5} + 94x^{4} - 2x^{3} - 13x^{2} - 77x + 47\)\(1\)\(37^{11}\)
\(\mathrm C_{12}\)12,2\(x^{12} + x^{11} + x^{10} + 27x^{9} + 27x^{8} - 90x^{7} + 53x^{6} + 1353x^{5} + 768x^{4} - 3886x^{3} + 1600x^{2} + 5409x + 1847\)\(3\)\(7^{8} 13^{11}\)
\(\mathrm C_{12}\)12,2\(x^{12} + x^{11} + 3x^{10} + 11x^{9} - 17x^{8} - 169x^{7} + 325x^{6} + 167x^{5} - 804x^{4} + 160x^{3} + 1102x^{2} - 780x + 1179\)\(1\)\(61^{11}\)
\(\mathrm D_6\)12,4\(x^{12} - 6x^{11} + 21x^{10} - 54x^{9} + 108x^{8} - 162x^{7} + 203x^{6} - 204x^{5} - 24x^{4} + 252x^{3} - 63x^{2} + 49\)\(1\)\(2^{8} 3^{14} 7^{6}\)
\(\mathrm D_6\)12,4\(x^{12} + 13x^{10} + 58x^{8} + 109x^{6} + 86x^{4} + 25x^{2} + 1\)\(1\)\(2^{16} 37^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 4x^{6} + 64\)\(1\)\(2^{8} 3^{18} 5^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 6x^{11} + 18x^{10} - 14x^{9} + 21x^{8} - 108x^{7} + 368x^{6} - 216x^{5} + 84x^{4} - 112x^{3} + 288x^{2} - 192x + 64\)\(1\)\(2^{12} 3^{14} 5^{8}\)
\(\mathrm D_6\)12,4\(x^{12} - 24x^{9} + 156x^{6} + 36x^{3} + 27\)\(1\)\(2^{18} 3^{22}\)
\(\mathrm D_6\)12,4\(x^{12} - 18x^{10} + 155x^{8} - 610x^{6} + 865x^{4} + 196x^{2} + 784\)\(1\)\(7^{6} 67^{6}\)
\(\mathrm D_6\)12,4\(x^{12} + 12x^{10} - 11x^{9} + 76x^{8} - 55x^{7} + 200x^{6} - 154x^{5} + 391x^{4} - 517x^{3} + 872x^{2} - 209x + 103\)\(1\)\(11^{6} 43^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 9x^{10} + 2x^{8} + 48x^{6} + 325x^{4} + 225x^{2} + 225\)\(1\)\(3^{6} 5^{8} 19^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 4x^{11} + 10x^{10} + 4x^{9} - 202x^{8} + 650x^{7} - 6x^{6} - 4020x^{5} + 9126x^{4} - 9968x^{3} + 8254x^{2} - 8510x + 7165\)\(2\)\(2^{12} 5^{6} 47^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 6x^{6} + 729\)\(2\)\(2^{12} 3^{22} 5^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 8x^{10} - 45x^{8} + 60x^{6} + 2857x^{4} + 6030x^{2} + 3844\)\(3\)\(2^{18} 7^{8} 11^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 22x^{10} + 191x^{8} - 1498x^{6} + 10537x^{4} - 26784x^{2} + 82944\)\(1\)\(2^{18} 163^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 4x^{11} + 8x^{10} + 12x^{9} - 225x^{8} + 726x^{7} - 1032x^{6} - 998x^{5} + 16965x^{4} - 66354x^{3} + 149058x^{2} - 195468x + 128164\)\(2\)\(2^{12} 7^{6} 61^{6}\)
\(\mathrm D_6\)12,4\(x^{12} + 27x^{10} + 9x^{9} + 243x^{8} + 486x^{7} + 288x^{6} - 1539x^{5} + 1647x^{4} + 711x^{3} - 972x^{2} - 4428x + 3816\)\(2\)\(3^{22} 5^{6} 7^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 12x^{10} - 92x^{9} + 57x^{8} + 996x^{7} + 2132x^{6} - 1920x^{5} - 12459x^{4} - 17944x^{3} + 9108x^{2} + 52272x + 58564\)\(2\)\(2^{18} 3^{14} 19^{6}\)
\(\mathrm D_6\)12,4\(x^{12} - 6x^{11} + 27x^{10} - 70x^{9} + 254x^{8} - 622x^{7} + 107x^{6} + 806x^{5} - 1245x^{4} + 7188x^{3} - 11884x^{2} - 12176x + 35044\)\(2\)\(2^{18} 3^{6} 5^{6} 11^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + x^{11} - x^{9} - x^{8} + x^{6} - x^{4} - x^{3} + x + 1\)\(1\)\(3^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)\(1\)\(2^{12} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{6} + 1\)\(1\)\(2^{12} 3^{18}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1\)\(1\)\(5^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 4x^{9} + 17x^{6} - 4x^{3} + 1\)\(1\)\(3^{18} 5^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1\)\(1\)\(2^{12} 3^{6} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 5x^{9} + 17x^{6} + 40x^{3} + 64\)\(1\)\(3^{18} 7^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{11} + 8x^{10} + 3x^{9} + 44x^{8} - 2x^{7} + 49x^{6} - 13x^{5} + 46x^{4} - 10x^{3} + 11x^{2} + 2x + 1\)\(1\)\(3^{6} 5^{6} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 2x^{10} + 4x^{8} - 8x^{6} + 16x^{4} - 32x^{2} + 64\)\(1\)\(2^{18} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 13x^{8} + 26x^{4} + 1\)\(1\)\(2^{24} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 8x^{6} + 64\)\(1\)\(2^{18} 3^{18}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{11} - 2x^{10} + 5x^{9} + x^{8} - 16x^{7} + 13x^{6} - 48x^{5} + 9x^{4} + 135x^{3} - 162x^{2} - 243x + 729\)\(1\)\(7^{10} 11^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 10x^{10} + 76x^{8} - 224x^{6} + 496x^{4} - 192x^{2} + 64\)\(1\)\(2^{18} 3^{6} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{11} - 3x^{10} + 7x^{9} + 5x^{8} - 33x^{7} + 13x^{6} - 132x^{5} + 80x^{4} + 448x^{3} - 768x^{2} - 1024x + 4096\)\(2\)\(3^{6} 5^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + x^{11} - 7x^{10} - 8x^{9} + 34x^{8} + 42x^{7} - 76x^{6} - 147x^{5} + 76x^{4} + 20x^{3} - 154x^{2} + 638x + 841\)\(2\)\(3^{6} 5^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + x^{11} - 16x^{10} - 27x^{9} + 92x^{8} + 133x^{7} - 42x^{6} - 224x^{5} + 241x^{4} - 895x^{3} + 900x^{2} + 88x + 181\)\(1\)\(3^{6} 7^{8} 11^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 15x^{10} + 92x^{8} - 302x^{6} + 596x^{4} - 792x^{2} + 841\)\(2\)\(2^{12} 5^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 6x^{11} + 39x^{10} - 140x^{9} + 447x^{8} - 1014x^{7} + 1867x^{6} - 2574x^{5} + 2703x^{4} - 2052x^{3} + 1077x^{2} - 348x + 53\)\(1\)\(2^{12} 3^{16} 7^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 12x^{10} + 54x^{8} - 130x^{6} + 213x^{4} - 198x^{2} + 361\)\(2\)\(2^{12} 3^{18} 5^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 3x^{10} + 18x^{8} + 64x^{6} + 109x^{4} + 39x^{2} + 49\)\(1\)\(2^{12} 19^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 4x^{11} - 17x^{10} - 74x^{9} + 86x^{8} + 444x^{7} - 31x^{6} - 750x^{5} - 75x^{4} + 324x^{3} + 554x^{2} + 234x + 97\)\(1\)\(2^{12} 7^{8} 11^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + 4x^{11} + 27x^{10} + 92x^{9} + 312x^{8} + 674x^{7} + 1132x^{6} + 1455x^{5} + 1638x^{4} + 2165x^{3} + 2575x^{2} + 2333x + 1117\)\(1\)\(3^{6} 7^{6} 13^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 14x^{9} + 161x^{6} + 392x^{3} + 343\)\(3\)\(3^{18} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 2x^{11} + 5x^{10} + 6x^{9} - 37x^{8} + 166x^{7} + 240x^{6} - 158x^{5} + 1285x^{4} + 1244x^{3} - 1698x^{2} + 2044x + 5329\)\(1\)\(2^{18} 3^{6} 13^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 4x^{11} - 23x^{10} + 94x^{9} + 177x^{8} - 740x^{7} - 427x^{6} + 1962x^{5} + 431x^{4} - 1644x^{3} + 945x^{2} - 172x + 421\)\(2\)\(2^{12} 3^{6} 5^{6} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 18x^{10} - 20x^{9} + 153x^{8} + 228x^{7} - 349x^{6} - 1152x^{5} + 600x^{4} - 1312x^{3} - 3600x^{2} + 7296x + 23104\)\(2\)\(3^{18} 5^{6} 7^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 30x^{10} + 368x^{8} - 2416x^{6} + 9536x^{4} - 25344x^{2} + 53824\)\(2\)\(2^{18} 5^{6} 7^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 4x^{10} - 15x^{8} - 56x^{6} + 470x^{4} + 516x^{2} + 961\)\(2\)\(2^{24} 13^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 4x^{11} - 32x^{10} + 124x^{9} + 387x^{8} - 1380x^{7} - 1970x^{6} + 5888x^{5} + 5456x^{4} - 10132x^{3} - 2764x^{2} + 4356x + 10961\)\(3\)\(2^{18} 7^{8} 11^{6}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - x^{11} - 3x^{10} - 50x^{9} - 28x^{8} + 276x^{7} + 399x^{6} + 1097x^{5} + 3163x^{4} + 1326x^{3} - 448x^{2} + 2200x + 1936\)\(1\)\(3^{6} 43^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 4x^{11} - 44x^{10} + 164x^{9} + 755x^{8} - 2468x^{7} - 6090x^{6} + 15640x^{5} + 26308x^{4} - 42932x^{3} - 49916x^{2} + 41324x + 79561\)\(2\)\(2^{18} 3^{6} 5^{6} 7^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 6x^{11} + 63x^{10} - 260x^{9} + 1225x^{8} - 3406x^{7} + 9165x^{6} - 16600x^{5} + 26314x^{4} - 28448x^{3} + 24160x^{2} - 12208x + 3992\)\(1\)\(2^{18} 7^{6} 13^{8}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} + x^{11} + 4x^{10} + 49x^{9} + 26x^{8} - 51x^{7} - 22x^{6} - 239x^{5} + 2782x^{4} + 5887x^{3} + 3488x^{2} - 642x + 337\)\(3\)\(7^{10} 13^{10}\)
\(\mathrm C_2\times \mathrm C_6\)12,5\(x^{12} - 6x^{11} + 53x^{10} - 210x^{9} + 845x^{8} - 2186x^{7} + 5105x^{6} - 8480x^{5} + 11479x^{4} - 10988x^{3} + 6685x^{2} - 2298x + 337\)\(2\)\(2^{12} 7^{6} 13^{10}\)
\(\mathrm C_{14}\)14,2\(x^{14} - 28x^{11} + 7x^{10} + 14x^{9} + 189x^{8} - 90x^{7} - 98x^{6} - 196x^{5} + 427x^{4} - 217x^{3} - 140x^{2} + 119x + 79\)\(1\)\(-7^{25}\)
\(\mathrm C_{14}\)14,2\(x^{14} + 2x^{13} + 8x^{12} - 20x^{11} + 72x^{10} - 47x^{9} + 122x^{8} - 81x^{7} + 1253x^{6} - 5872x^{5} + 10822x^{4} - 2784x^{3} - 7477x^{2} - 1245x + 6529\)\(1\)\(-43^{13}\)
\(\mathrm C_{16}\)16,1\(x^{16} + x^{15} + x^{14} + x^{13} + x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\)\(1\)\(17^{15}\)
\(\mathrm C_4^2\)16,2\(x^{16} - 4x^{14} + 14x^{12} - 48x^{10} + 164x^{8} - 96x^{6} + 56x^{4} - 32x^{2} + 16\)\(1\)\(2^{44} 5^{12}\)
\(\mathrm C_4^2\)16,2\(x^{16} + x^{15} - x^{14} - 7x^{13} - 12x^{12} - 13x^{11} + 42x^{10} + 137x^{9} + 141x^{8} - 262x^{7} + 269x^{6} - 182x^{5} - 95x^{4} - 21x^{3} + 90x^{2} - 108x + 81\)\(1\)\(5^{12} 13^{12}\)
\(\mathrm C_2^2\rtimes \mathrm C_4\)16,3\(x^{16} - 4x^{14} + 27x^{12} + 52x^{10} + 189x^{8} + 902x^{6} + 928x^{4} - 3880x^{2} + 2704\)\(1\)\(2^{24} 17^{12}\)
\(\mathrm C_2^2\rtimes \mathrm C_4\)16,3\(x^{16} + 10x^{15} + 54x^{14} + 182x^{13} + 443x^{12} + 924x^{11} + 1972x^{10} + 3847x^{9} + 4642x^{8} + 738x^{7} - 4735x^{6} - 784x^{5} + 14550x^{4} + 29227x^{3} + 29554x^{2} + 16791x + 5391\)\(1\)\(13^{12} 17^{8}\)
\(\mathrm C_2\times \mathrm C_8\)16,5\(x^{16} + 1\)\(1\)\(2^{64}\)
\(\mathrm C_2\times \mathrm C_8\)16,5\(x^{16} - 8x^{14} + 44x^{12} - 128x^{10} + 270x^{8} - 288x^{6} + 216x^{4} - 32x^{2} + 4\)\(1\)\(2^{62} 3^{8}\)
\(\mathrm C_2\times \mathrm C_8\)16,5\(x^{16} - 16x^{14} + 104x^{12} - 352x^{10} + 660x^{8} - 672x^{6} + 336x^{4} - 64x^{2} + 2209\)\(2\)\(2^{64} 5^{8}\)
\(\mathrm D_8\)16,7\(x^{16} - 4x^{15} + 27x^{14} - 84x^{13} + 237x^{12} - 336x^{11} + 308x^{10} - 134x^{9} + 432x^{8} - 306x^{7} - 421x^{6} + 1317x^{5} - 36x^{4} - 805x^{3} + 295x^{2} + 475x + 125\)\(1\)\(5^{8} 101^{8}\)
\(\mathrm D_8\)16,7\(x^{16} + 2x^{14} + 53x^{12} + 354x^{10} + 1160x^{8} + 1833x^{6} + 2729x^{4} + 2678x^{2} + 8281\)\(1\)\(13^{8} 53^{8}\)
\(\mathrm D_8\)16,7\(x^{16} + 6x^{15} + 39x^{14} + 133x^{13} + 472x^{12} + 1069x^{11} + 2329x^{10} + 3680x^{9} + 5042x^{8} + 4897x^{7} + 4450x^{6} - 3707x^{5} + 1064x^{4} - 11129x^{3} + 8318x^{2} - 1688x + 107\)\(1\)\(13^{8} 61^{8}\)
\(\mathrm D_8\)16,7\(x^{16} + 2x^{15} + 17x^{14} + 35x^{13} + 142x^{12} + 269x^{11} + 619x^{10} + 842x^{9} + 1392x^{8} + 1203x^{7} + 152x^{6} - 111x^{5} + 414x^{4} - 2457x^{3} + 405x^{2} + 3645x + 6561\)\(1\)\(5^{8} 181^{8}\)
\(\mathrm D_8\)16,7\(x^{16} + 6x^{14} - 49x^{12} + 118x^{10} + 2133x^{8} - 15444x^{6} + 25700x^{4} + 52512x^{2} + 43264\)\(3\)\(2^{24} 257^{8}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1\)\(1\)\(2^{16} 3^{8} 5^{12}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} - x^{12} + x^{8} - x^{4} + 1\)\(1\)\(2^{32} 5^{12}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} - x^{8} + 1\)\(1\)\(2^{48} 3^{8}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} - x^{15} + 2x^{14} - 5x^{13} + 5x^{12} + x^{11} + 6x^{10} + 5x^{9} - 21x^{8} + 10x^{7} + 24x^{6} + 8x^{5} + 80x^{4} - 160x^{3} + 128x^{2} - 128x + 256\)\(1\)\(3^{8} 5^{12} 7^{8}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} + 2x^{14} - 8x^{10} - 16x^{8} - 32x^{6} + 128x^{2} + 256\)\(1\)\(2^{24} 3^{8} 5^{12}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} + 3x^{14} + 5x^{12} + 3x^{10} - 11x^{8} + 12x^{6} + 80x^{4} + 192x^{2} + 256\)\(1\)\(2^{16} 5^{12} 7^{8}\)
\(\mathrm C_2^2\times \mathrm C_4\)16,10\(x^{16} + 47x^{8} + 1\)\(1\)\(2^{48} 5^{8}\)
\(\mathrm C_2\times \mathrm D_4\)16,11\(x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256\)\(1\)\(2^{16} 3^{12} 11^{8}\)
\(\mathrm C_2\times \mathrm D_4\)16,11\(x^{16} + 4x^{15} - 28x^{13} - 54x^{12} + 12x^{11} + 220x^{10} + 428x^{9} + 378x^{8} - 44x^{7} - 632x^{6} - 1068x^{5} - 714x^{4} + 316x^{3} + 828x^{2} + 380x + 73\)\(1\)\(2^{44} 3^{12}\)
\(\mathrm C_2\times \mathrm D_4\)16,11\(x^{16} - 14x^{14} + 91x^{12} - 322x^{10} + 1053x^{8} - 644x^{6} + 364x^{4} - 112x^{2} + 16\)\(1\)\(2^{24} 3^{8} 17^{8}\)
\(\mathrm C_2\times \mathrm D_4\)16,11\(x^{16} - 6x^{15} + 21x^{14} - 50x^{13} + 96x^{12} - 186x^{11} + 445x^{10} - 1198x^{9} + 2495x^{8} - 2836x^{7} + 694x^{6} - 2800x^{5} + 17264x^{4} - 35936x^{3} + 53912x^{2} - 57728x + 26896\)\(1\)\(2^{24} 5^{8} 17^{8}\)
\(\mathrm C_2\times Q_8\)16,12\(x^{16} - 12x^{14} + 108x^{12} - 360x^{10} + 855x^{8} - 1080x^{6} + 972x^{4} - 324x^{2} + 81\)\(1\)\(2^{48} 3^{12}\)
\(\mathrm C_4\circ \mathrm D_4\)16,13\(x^{16} + 4x^{15} + 4x^{14} + 88x^{13} + 482x^{12} + 1240x^{11} + 4866x^{10} + 16798x^{9} + 22609x^{8} - 13608x^{7} - 35878x^{6} + 1878x^{5} + 155441x^{4} + 552526x^{3} + 946711x^{2} + 797118x + 362969\)\(1\)\(2^{24} 5^{8} 37^{8}\)
\(\mathrm C_{18}\)18,2\(x^{18} + x^{9} + 1\)\(1\)\(-3^{45}\)
\(\mathrm C_{18}\)18,2\(x^{18} + x^{17} + x^{16} + x^{15} + x^{14} + x^{13} + x^{12} + x^{11} + x^{10} + x^{9} + x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\)\(1\)\(-19^{17}\)
\(\mathrm C_3\times \mathrm C_6\)18,5\(x^{18} + 4x^{15} + 27x^{12} - 42x^{9} + 125x^{6} + 11x^{3} + 1\)\(1\)\(-3^{27} 7^{12}\)
\(\mathrm C_{20}\)20,2\(x^{20} + x^{15} + x^{10} + x^{5} + 1\)\(1\)\(5^{35}\)
\(\mathrm D_{10}\)20,4\(x^{20} + 6x^{19} + 33x^{18} + 109x^{17} + 332x^{16} + 706x^{15} + 1299x^{14} + 1910x^{13} + 3303x^{12} + 7116x^{11} + 14445x^{10} + 24009x^{9} + 30102x^{8} + 37094x^{7} + 54187x^{6} + 82991x^{5} + 119418x^{4} + 148247x^{3} + 185442x^{2} + 184250x + 112225\)\(1\)\(19^{10} 43^{10}\)
\(\mathrm D_{10}\)20,4\(x^{20} - 55x^{16} + 1040x^{14} + 17860x^{12} + 74434x^{10} + 191605x^{8} + 137080x^{6} + 1950225x^{4} + 2274430x^{2} + 1493284\)\(2\)\(2^{30} 5^{26} 7^{10}\)
\(\mathrm C_2\times \mathrm C_{10}\)20,5\(x^{20} + x^{19} - x^{17} - x^{16} + x^{14} + x^{13} - x^{11} - x^{10} - x^{9} + x^{7} + x^{6} - x^{4} - x^{3} + x + 1\)\(1\)\(3^{10} 11^{18}\)
\(\mathrm C_2\times \mathrm C_{10}\)20,5\(x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)\(1\)\(2^{20} 11^{18}\)
\(\mathrm C_2\times \mathrm C_{10}\)20,5\(x^{20} - 9x^{18} + 53x^{16} - 182x^{14} + 454x^{12} - 711x^{10} + 796x^{8} - 469x^{6} + 190x^{4} - 15x^{2} + 1\)\(1\)\(2^{20} 3^{10} 11^{16}\)
\({\rm SL}_2({\mathbb F}_3)\)24,3\(x^{24} - 3x^{23} - 2x^{22} + 16x^{21} - 12x^{20} + 52x^{19} - 324x^{18} - 436x^{17} + 3810x^{16} - 1638x^{15} - 8012x^{14} - 12988x^{13} + 67224x^{12} - 76152x^{11} + 41175x^{10} - 39587x^{9} + 70068x^{8} - 66440x^{7} + 38488x^{6} - 23248x^{5} + 16672x^{4} - 6976x^{3} + 2816x^{2} - 1280x + 512\)\(1\)\(163^{16}\)
\(\mathrm C_4\times \mathfrak S_3\)24,5\(x^{24} - 9x^{23} + 32x^{22} - 51x^{21} + 31x^{20} - 29x^{19} + 156x^{18} - 78x^{17} - 721x^{16} + 581x^{15} + 1632x^{14} + 52x^{13} - 4036x^{12} - 3592x^{11} + 7622x^{10} + 8664x^{9} - 6756x^{8} - 10837x^{7} - 79x^{6} + 6384x^{5} + 5361x^{4} + 76x^{3} - 978x^{2} - 66x + 121\)\(1\)\(2^{16} 5^{22} 13^{12}\)
\(\mathrm D_{12}\)24,6\(x^{24} + 4x^{23} + 18x^{22} + 87x^{21} + 421x^{20} + 817x^{19} + 916x^{18} - 760x^{17} + 2653x^{16} - 10930x^{15} + 21120x^{14} - 11863x^{13} + 10673x^{12} - 13730x^{11} + 47096x^{10} - 18513x^{9} + 20043x^{8} - 16868x^{7} - 3184x^{6} - 1140x^{5} + 3178x^{4} + 754x^{3} - 940x^{2} - 13x + 89\)\(1\)\(5^{12} 269^{12}\)
\(\mathrm C_2\times \mathrm C_{12}\)24,9\(x^{24} + x^{23} - x^{19} - x^{18} - x^{17} - x^{16} + x^{14} + x^{13} + x^{12} + x^{11} + x^{10} - x^{8} - x^{7} - x^{6} - x^{5} + x + 1\)\(1\)\(5^{18} 7^{20}\)
\(\mathrm C_2\times \mathrm C_{12}\)24,9\(x^{24} + x^{21} - x^{15} - x^{12} - x^{9} + x^{3} + 1\)\(1\)\(3^{36} 5^{18}\)
\(\mathrm C_2\times \mathrm C_{12}\)24,9\(x^{24} - x^{23} - 2x^{22} + 5x^{21} - 4x^{20} + 8x^{19} + 15x^{18} - 59x^{17} + 26x^{16} + 114x^{15} + 34x^{14} - 119x^{13} - 10x^{12} - 196x^{11} - 198x^{10} + 289x^{9} + 559x^{8} - 307x^{7} + 22x^{6} + 46x^{5} - 22x^{4} + 12x^{3} - x^{2} - 2x + 1\)\(1\)\(3^{12} 5^{18} 7^{16}\)
\(\mathrm C_3\times \mathrm D_4\)24,10\(x^{24} - 9x^{23} + 32x^{22} - 66x^{21} + 110x^{20} - 206x^{19} + 432x^{18} + 453x^{17} - 1211x^{16} - 5141x^{15} - 15772x^{14} + 15555x^{13} + 135453x^{12} + 139187x^{11} - 257205x^{10} - 746717x^{9} - 263031x^{8} + 1400496x^{7} + 2733470x^{6} + 2554259x^{5} + 1494862x^{4} + 663853x^{3} + 353517x^{2} + 197082x + 84499\)\(1\)\(13^{20} 17^{12}\)
\(\mathrm C_2\times \mathfrak A_4\)24,13\(x^{24} + 6x^{23} + 19x^{22} + 42x^{21} + 65x^{20} + 44x^{19} - 200x^{18} - 855x^{17} - 1546x^{16} - 689x^{15} + 3945x^{14} + 9900x^{13} + 15159x^{12} + 14980x^{11} + 20470x^{10} + 17686x^{9} + 24937x^{8} + 29458x^{7} + 30778x^{6} + 23258x^{5} + 14574x^{4} + 5951x^{3} + 1908x^{2} + 649x + 121\)\(1\)\(3^{12} 61^{16}\)
\(\mathrm C_2\times \mathfrak A_4\)24,13\(x^{24} + 4x^{23} + 21x^{20} - 140x^{19} - 144x^{18} + 720x^{17} - 417x^{16} - 1688x^{15} + 3316x^{14} + 72x^{13} - 2759x^{12} + 4428x^{11} - 3522x^{10} + 1240x^{9} + 7105x^{8} - 14420x^{7} + 18534x^{6} - 14624x^{5} + 8263x^{4} - 3152x^{3} + 858x^{2} - 72x + 4\)\(1\)\(2^{36} 31^{16}\)
\(\mathrm C_2^2\times \mathfrak S_3\)24,14\(x^{24} - 12x^{23} + 78x^{22} - 340x^{21} + 1095x^{20} - 2748x^{19} + 5638x^{18} - 10026x^{17} + 16380x^{16} - 25084x^{15} + 34446x^{14} - 41352x^{13} + 48825x^{12} - 66672x^{11} + 85212x^{10} - 59258x^{9} - 1692x^{8} - 14544x^{7} + 92404x^{6} - 47388x^{5} - 83937x^{4} + 88840x^{3} + 5772x^{2} - 43566x + 18769\)\(1\)\(2^{32} 3^{28} 7^{12}\)
\(\mathrm C_2^2\times \mathrm C_6\)24,15\(x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1\)\(1\)\(2^{24} 3^{12} 7^{20}\)
\(\mathrm C_2^2\times \mathrm C_6\)24,15\(x^{24} - x^{23} - x^{22} + 4x^{21} - 4x^{20} - 4x^{19} + 17x^{18} + 12x^{17} - 46x^{16} + 43x^{15} + 44x^{14} - 188x^{13} + 189x^{12} + 188x^{11} + 44x^{10} - 43x^{9} - 46x^{8} - 12x^{7} + 17x^{6} + 4x^{5} - 4x^{4} - 4x^{3} - x^{2} + x + 1\)\(1\)\(3^{12} 5^{12} 7^{20}\)
\(\mathrm C_2^2\rtimes \mathrm C_8\)32,5\(x^{32} - 4x^{31} + 10x^{30} + 150x^{28} - 484x^{27} + 1290x^{26} + 332x^{25} + 6797x^{24} - 10156x^{23} + 32928x^{22} + 45672x^{21} + 150325x^{20} - 54628x^{19} + 268716x^{18} + 645284x^{17} + 1404151x^{16} - 448940x^{15} - 2976140x^{14} - 4612624x^{13} - 599552x^{12} + 4399140x^{11} + 6786614x^{10} + 3071008x^{9} - 884241x^{8} - 2543532x^{7} - 1018052x^{6} + 30728x^{5} + 369232x^{4} + 151840x^{3} + 201784x^{2} + 149760x + 67472\)\(1\)\(2^{48} 17^{28}\)
\(\mathrm C_2\times \mathrm C_4\rtimes \mathrm C_4\)32,23\(x^{32} - 8x^{30} + 20x^{28} - 96x^{26} + 248x^{24} + 1256x^{22} - 284x^{20} + 4320x^{18} - 31058x^{16} - 4344x^{14} + 164812x^{12} - 147392x^{10} - 54376x^{8} - 138408x^{6} + 333116x^{4} - 49408x^{2} + 5329\)\(1\)\(2^{108} 3^{24}\)
\(\mathrm C_2\times \mathrm{M}_4(2)\)32,37\(x^{32} - 8x^{31} + 40x^{30} - 180x^{29} + 694x^{28} - 2312x^{27} + 6908x^{26} - 18252x^{25} + 42936x^{24} - 89856x^{23} + 166568x^{22} - 271092x^{21} + 378194x^{20} - 434016x^{19} + 364428x^{18} - 112172x^{17} - 301690x^{16} + 734040x^{15} - 939336x^{14} + 732052x^{13} - 175390x^{12} - 395304x^{11} + 619428x^{10} - 445780x^{9} + 123392x^{8} + 68432x^{7} - 80520x^{6} + 29684x^{5} + 6838x^{4} - 7696x^{3} + 3604x^{2} - 20x + 241\)\(1\)\(2^{80} 5^{28}\)
\(\mathrm C_4\circ \mathrm D_8\)32,42\(x^{32} - 34x^{30} - 26x^{29} + 492x^{28} + 870x^{27} - 3573x^{26} - 12628x^{25} + 9322x^{24} + 100138x^{23} + 55561x^{22} - 454856x^{21} - 649046x^{20} + 1122990x^{19} + 3331294x^{18} - 1613322x^{17} - 11467988x^{16} + 5334934x^{15} + 24211061x^{14} - 22377862x^{13} - 18652088x^{12} + 28943112x^{11} + 772460x^{10} + 4154156x^{9} - 14650623x^{8} - 14479580x^{7} + 14160985x^{6} - 644332x^{5} + 17702092x^{4} - 6526030x^{3} + 6436934x^{2} - 935704x + 2307361\)\(1\)\(2^{48} 5^{16} 29^{16}\)
\(\mathfrak S_3\times \mathrm C_6\)36,12\(x^{36} + 18x^{35} + 162x^{34} + 954x^{33} + 4095x^{32} + 13617x^{31} + 36495x^{30} + 80829x^{29} + 148995x^{28} + 223803x^{27} + 254025x^{26} + 163836x^{25} - 83709x^{24} - 399645x^{23} - 572841x^{22} - 441990x^{21} - 87246x^{20} + 247977x^{19} + 401193x^{18} + 396441x^{17} + 328194x^{16} + 176364x^{15} + 12204x^{14} - 41148x^{13} - 37773x^{12} - 21735x^{11} - 31131x^{10} - 32643x^{9} - 3429x^{8} + 5157x^{7} + 11340x^{6} + 513x^{5} + 2916x^{4} + 405x^{3} + 216x^{2} - 108x + 9\)\(1\)\(2^{24} 3^{66} 5^{18}\)
\(\mathfrak S_3\times \mathrm C_6\)36,12\(x^{36} - 9x^{35} + 45x^{34} - 165x^{33} + 567x^{32} - 1821x^{31} + 4932x^{30} - 10431x^{29} + 16086x^{28} - 15373x^{27} - 2529x^{26} + 49287x^{25} - 105618x^{24} + 101700x^{23} + 32340x^{22} - 190539x^{21} + 120996x^{20} + 50193x^{19} - 1039x^{18} - 68310x^{17} - 142350x^{16} + 110586x^{15} + 160344x^{14} + 83628x^{13} - 55908x^{12} - 127872x^{11} - 76128x^{10} - 28592x^{9} + 41184x^{8} + 77424x^{7} + 58896x^{6} + 24768x^{5} + 4800x^{4} + 576x^{3} + 576x^{2} + 192x + 64\)\(1\)\(2^{24} 3^{62} 7^{18}\)
\(\mathfrak S_3\times \mathrm C_6\)36,12\(x^{36} - 6x^{34} + 41x^{32} - 68x^{30} + 234x^{28} - 1412x^{26} + 6532x^{24} + 20758x^{22} - 229771x^{20} + 354774x^{18} + 2807495x^{16} - 10673442x^{14} + 8064769x^{12} + 2622208x^{10} + 4534496x^{8} - 1216168x^{6} + 3044160x^{4} - 705024x^{2} + 46656\)\(1\)\(2^{54} 7^{24} 11^{18}\)
\(\mathrm C_2\times \mathrm F_5\)40,12\(x^{40} + 5x^{39} + 5x^{38} + 10x^{37} + 120x^{36} + 335x^{35} + 385x^{34} + 880x^{33} + 3945x^{32} + 9445x^{31} + 13377x^{30} + 21520x^{29} + 58640x^{28} + 138020x^{27} + 234210x^{26} + 332720x^{25} + 582480x^{24} + 1325105x^{23} + 2571315x^{22} + 3532260x^{21} + 3645749x^{20} + 5441460x^{19} + 16653210x^{18} + 45541900x^{17} + 88716195x^{16} + 123449190x^{15} + 118595340x^{14} + 62676300x^{13} - 16293100x^{12} - 67504200x^{11} - 61439572x^{10} - 16429490x^{9} + 21829825x^{8} + 26617315x^{7} + 10231975x^{6} - 2063290x^{5} - 2809025x^{4} + 91140x^{3} + 971640x^{2} + 460350x + 77841\)\(1\)\(2^{32} 5^{46} 7^{20}\)
\(\mathrm D_4\rtimes \mathfrak S_3\)48,15\(x^{48} - 16x^{47} + 154x^{46} - 1062x^{45} + 5861x^{44} - 27032x^{43} + 108118x^{42} - 382247x^{41} + 1216320x^{40} - 3519040x^{39} + 9354487x^{38} - 22981410x^{37} + 52537749x^{36} - 112139241x^{35} + 224599406x^{34} - 422866886x^{33} + 751689957x^{32} - 1262741576x^{31} + 2014037588x^{30} - 3052638118x^{29} + 4423121908x^{28} - 6134222492x^{27} + 8194638050x^{26} - 10554045180x^{25} + 13166769236x^{24} - 15909389418x^{23} + 18637913584x^{22} - 21183975650x^{21} + 23316032723x^{20} - 24826123460x^{19} + 25455052543x^{18} - 25225507043x^{17} + 24074543095x^{16} - 21881216430x^{15} + 19020997095x^{14} - 15911316338x^{13} + 12715024536x^{12} - 9328992351x^{11} + 6682355760x^{10} - 4672449816x^{9} + 2802278711x^{8} - 1633037848x^{7} + 958754217x^{6} - 529620206x^{5} + 181598936x^{4} - 53495044x^{3} + 99083410x^{2} + 28884359x + 7724261\)\(1\)\(2^{32} 5^{24} 101^{24}\)
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