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Label Polynomial Discriminant Galois group Class group
6.0.54208.1 x6 - 2x5 + 3x4 - 2x3 + 3x2 - 2x + 1 \( -\,2^{6}\cdot 7\cdot 11^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.87616.1 x6 - x4 - 2x3 - x2 + 1 \( 2^{6}\cdot 37^{2} \) $S_4$ (as 6T7) trivial
6.2.118336.1 x6 - 2x5 + 3x4 - 6x3 + 3x2 - 2x + 1 \( 2^{6}\cdot 43^{2} \) $S_4$ (as 6T7) trivial
6.2.131648.1 x6 - 2x5 + 2x4 + 2x3 - 6x2 + 6x - 2 \( 2^{6}\cdot 11^{2}\cdot 17 \) $S_4\times C_2$ (as 6T11) trivial
6.0.141248.1 x6 + x4 + x2 - 2x + 1 \( -\,2^{6}\cdot 2207 \) $S_6$ (as 6T16) trivial
6.0.198592.1 x6 - 2x3 + 2x2 - 2x + 2 \( -\,2^{6}\cdot 29\cdot 107 \) $S_6$ (as 6T16) trivial
6.2.202304.1 x6 - 2x5 + 3x4 - 3x2 + 4x - 1 \( 2^{6}\cdot 29\cdot 109 \) $S_6$ (as 6T16) trivial
6.2.207936.1 x6 - 2x5 + x4 + 2x3 - x2 - 2x - 1 \( 2^{6}\cdot 3^{2}\cdot 19^{2} \) $S_4$ (as 6T7) trivial
6.2.297536.1 x6 - 3x4 + x2 - 2x + 1 \( 2^{6}\cdot 4649 \) $S_6$ (as 6T16) trivial
6.2.299072.1 x6 - 2x5 + 2x4 - 2x2 + 2x - 2 \( 2^{6}\cdot 4673 \) $S_6$ (as 6T16) trivial
6.0.303040.1 x6 - 2x5 + 2x4 - 2x3 + 2x2 - 2x + 2 \( -\,2^{6}\cdot 5\cdot 947 \) $S_6$ (as 6T16) trivial
6.2.307264.1 x6 - 2x5 + 2x2 - 2x + 2 \( 2^{6}\cdot 4801 \) $S_6$ (as 6T16) trivial
6.2.317504.1 x6 - 2x5 - 3x4 + 6x3 + 3x2 - 2x - 1 \( 2^{6}\cdot 11^{2}\cdot 41 \) $S_4\times C_2$ (as 6T11) trivial
6.2.348736.1 x6 - x4 - 2x3 - 5x2 - 4x - 3 \( 2^{6}\cdot 5449 \) $S_6$ (as 6T16) trivial
6.0.356800.1 x6 - 2x5 + 6x4 - 8x3 + 10x2 - 6x + 2 \( -\,2^{6}\cdot 5^{2}\cdot 223 \) $S_6$ (as 6T16) trivial
6.2.361024.1 x6 - 2x5 + 3x4 - 4x3 + x2 - 1 \( 2^{6}\cdot 5641 \) $S_6$ (as 6T16) trivial
6.0.363968.1 x6 - 2x5 + 6x4 - 4x3 + 6x2 + 2x + 2 \( -\,2^{6}\cdot 11^{2}\cdot 47 \) $S_4\times C_2$ (as 6T11) trivial
6.0.363968.2 x6 - 2x5 - x4 + 4x3 + x2 - 8x + 7 \( -\,2^{6}\cdot 11^{2}\cdot 47 \) $S_4\times C_2$ (as 6T11) trivial
6.2.379456.1 x6 - 2x5 + 3x4 - 8x3 + 9x2 - 4x - 1 \( 2^{6}\cdot 7^{2}\cdot 11^{2} \) $S_4$ (as 6T7) trivial
6.2.386624.1 x6 - 2x5 + x4 - 4x3 + 5x2 + 1 \( 2^{6}\cdot 7\cdot 863 \) $S_6$ (as 6T16) trivial
6.2.406592.1 x6 - 2x5 + 2x4 - 2x3 - 2x2 + 2x + 2 \( 2^{6}\cdot 6353 \) $S_6$ (as 6T16) trivial
6.0.440256.1 x6 - 2x5 + 3x4 - 2x3 - x2 + 2x + 1 \( -\,2^{6}\cdot 3\cdot 2293 \) $S_6$ (as 6T16) trivial
6.0.454592.1 x6 - 2x5 + 4x3 - 4x + 4 \( -\,2^{6}\cdot 7103 \) $S_6$ (as 6T16) trivial
6.2.461376.1 x6 - x4 - 2x3 + 3x2 + 4x + 1 \( 2^{6}\cdot 3^{4}\cdot 89 \) $S_6$ (as 6T16) trivial
6.2.479296.1 x6 + 3x4 - 2x3 - x2 + 4x + 1 \( 2^{6}\cdot 7489 \) $S_6$ (as 6T16) trivial
6.4.507328.1 x6 - 2x5 - x4 + 2x3 - x2 + 2x + 1 \( -\,2^{6}\cdot 7927 \) $S_6$ (as 6T16) trivial
6.2.510528.1 x6 - 2x5 + 2x4 - 6x2 + 6x - 2 \( 2^{6}\cdot 3\cdot 2659 \) $S_6$ (as 6T16) trivial
6.2.524864.1 x6 - x4 + x2 - 2x - 1 \( 2^{6}\cdot 59\cdot 139 \) $S_6$ (as 6T16) trivial
6.2.529984.1 x6 + x4 - 2x3 - x2 - 1 \( 2^{6}\cdot 7^{2}\cdot 13^{2} \) $S_4$ (as 6T7) trivial
6.0.531392.1 x6 - 2x5 + 6x4 - 10x3 + 10x2 - 6x + 2 \( -\,2^{6}\cdot 19^{2}\cdot 23 \) $S_4\times C_2$ (as 6T11) trivial
6.0.531392.2 x6 - x4 - 4x3 + x2 + 2x + 3 \( -\,2^{6}\cdot 19^{2}\cdot 23 \) $S_4\times C_2$ (as 6T11) trivial
6.0.548800.1 x6 - 2x5 - 2x4 + 6x3 + 2x2 - 6x + 2 \( -\,2^{6}\cdot 5^{2}\cdot 7^{3} \) $S_4\times C_2$ (as 6T11) trivial
6.0.558016.1 x6 - 2x3 - 2x2 + 2x + 2 \( -\,2^{6}\cdot 8719 \) $S_6$ (as 6T16) trivial
6.2.564288.1 x6 - 2x5 + 2x4 - 4x3 + 2x2 - 2x + 2 \( 2^{6}\cdot 3\cdot 2939 \) $S_6$ (as 6T16) trivial
6.2.565312.1 x6 - 2x5 + 4x4 - 8x3 + 2x2 - 2x - 2 \( 2^{6}\cdot 11^{2}\cdot 73 \) $S_4\times C_2$ (as 6T11) trivial
6.0.589760.1 x6 - 2x5 + 4x4 - 4x3 + 6x2 - 2x + 2 \( -\,2^{6}\cdot 5\cdot 19\cdot 97 \) $S_6$ (as 6T16) trivial
6.2.641600.1 x6 - 2x5 + 2x3 - 2x2 + 2x - 2 \( 2^{6}\cdot 5^{2}\cdot 401 \) $S_6$ (as 6T16) trivial
6.2.652864.1 x6 - 2x5 - x4 + 2x3 - x2 - 2x + 1 \( 2^{6}\cdot 101^{2} \) $S_4$ (as 6T7) trivial
6.2.666176.1 x6 - 2x5 - x4 + 4x3 + x2 - 4x - 1 \( 2^{6}\cdot 7\cdot 1487 \) $S_6$ (as 6T16) trivial
6.0.680384.1 x6 - 2x5 + 4x4 - 4x3 + 6x2 - 6x + 2 \( -\,2^{6}\cdot 10631 \) $S_6$ (as 6T16) trivial
6.2.686144.1 x6 - 2x5 + 4x4 - 6x3 + 6x2 - 6x + 2 \( 2^{6}\cdot 71\cdot 151 \) $S_6$ (as 6T16) trivial
6.2.697408.1 x6 - 2x5 - x4 + 5x2 - 1 \( 2^{6}\cdot 17\cdot 641 \) $S_6$ (as 6T16) trivial
6.0.699840.1 x6 + 3x4 - 2x3 + 3x2 + 1 \( -\,2^{6}\cdot 3^{7}\cdot 5 \) $S_4\times C_2$ (as 6T11) $[2]$
6.0.716224.2 x6 + 2x4 + 2x2 - 2x + 6 \( -\,2^{6}\cdot 19^{2}\cdot 31 \) $S_4\times C_2$ (as 6T11) trivial
6.0.716736.1 x6 - 2x5 + 5x4 - 6x3 + 7x2 - 6x + 3 \( -\,2^{6}\cdot 3\cdot 3733 \) $S_6$ (as 6T16) trivial
6.0.721344.1 x6 - 2x5 + 4x4 - 4x3 + 4 \( -\,2^{6}\cdot 3\cdot 13\cdot 17^{2} \) $S_6$ (as 6T16) trivial
6.2.743488.1 x6 + 2x4 - 4x3 + 6x2 - 6x + 2 \( 2^{6}\cdot 11617 \) $S_6$ (as 6T16) trivial
6.0.744896.1 x6 - 2x5 + 6x4 - 4x3 + 6x2 - 2x + 2 \( -\,2^{6}\cdot 103\cdot 113 \) $S_6$ (as 6T16) trivial
6.4.793024.1 x6 - 4x4 - 2x3 + 6x2 + 2x - 2 \( -\,2^{6}\cdot 12391 \) $S_6$ (as 6T16) trivial
6.2.793152.1 x6 - 3x4 - 2x3 + 3x2 - 1 \( 2^{6}\cdot 3^{6}\cdot 17 \) $S_4\times C_2$ (as 6T11) trivial
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