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Label Polynomial Discriminant Galois group Class group
6.2.8155037.1 x6 - x5 - x4 - 2x3 - 2x2 + 7x - 3 \( 11^{4}\cdot 557 \) $S_6$ (as 6T16) trivial
6.2.8799241.1 x6 - 2x5 + 2x4 + 9x3 - 24x2 + 31x - 12 \( 11^{4}\cdot 601 \) $S_6$ (as 6T16) trivial
6.4.9077420.1 x6 - x5 - 8x4 - x3 + 10x2 + 6x + 2 \( -\,2^{2}\cdot 5\cdot 11^{4}\cdot 31 \) $S_6$ (as 6T16) trivial
6.2.10731853.1 x6 - x5 + 3x4 - x3 - x2 - 5x + 2 \( 11^{4}\cdot 733 \) $S_6$ (as 6T16) trivial
6.0.19370043.1 x6 - 3x5 + 4x4 + 8x3 - 17x2 + 7x + 31 \( -\,3^{3}\cdot 7^{2}\cdot 11^{4} \) $S_3\times C_3$ (as 6T5) trivial
6.2.30219024.1 x6 - x5 - 5x4 + 8x3 - 7x2 + 13x - 5 \( 2^{4}\cdot 3\cdot 11^{4}\cdot 43 \) $S_6$ (as 6T16) trivial
6.0.36939243.1 x6 - 2x5 - x4 + 2x3 + 2x2 + 3x + 3 \( -\,3\cdot 11^{4}\cdot 29^{2} \) $S_6$ (as 6T16) $[2]$
6.0.44040128.2 x6 - 2x5 + 7x4 - 16x3 + 34x2 - 40x + 28 \( -\,2^{6}\cdot 11^{4}\cdot 47 \) $S_6$ (as 6T16) trivial
6.2.53410368.1 x6 - 2x5 + 2x4 - 2x3 + 9x2 + 20x - 1 \( 2^{6}\cdot 3\cdot 11^{4}\cdot 19 \) $S_6$ (as 6T16) trivial
6.0.66806883.2 x6 - 3x5 + 4x4 + 52x3 - 83x2 + 29x + 757 \( -\,3^{3}\cdot 11^{4}\cdot 13^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.2.68402752.2 x6 - 2x5 - 4x4 + 6x3 + x2 + 4x - 16 \( 2^{6}\cdot 11^{4}\cdot 73 \) $S_6$ (as 6T16) trivial
6.0.79456707.1 x6 - x5 + 14x4 - 12x3 + 10x2 - 5x + 2 \( -\,3^{4}\cdot 11^{4}\cdot 67 \) $S_6$ (as 6T16) trivial
6.0.85371671.1 x6 - x5 - 2x4 - 5x3 + 15x2 - 15x + 14 \( -\,7^{3}\cdot 11^{4}\cdot 17 \) $S_6$ (as 6T16) trivial
6.0.90525303.1 x6 - x5 + 19x4 + 14x3 + 95x2 + 195x + 301 \( -\,3^{3}\cdot 11^{4}\cdot 229 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.98504648.1 x6 - x5 + 3x4 - 23x3 + 43x2 - 16x - 20 \( 2^{3}\cdot 11^{4}\cdot 29^{2} \) $S_6$ (as 6T16) trivial
6.0.107918811.1 x6 - x5 - 14x4 + 3x3 + 117x2 + 228x + 147 \( -\,3^{4}\cdot 7\cdot 11^{4}\cdot 13 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.111637625.1 x6 - 3x5 + 10x4 - 15x3 + 5x2 - 9x + 7 \( 5^{3}\cdot 11^{4}\cdot 61 \) $S_6$ (as 6T16) trivial
6.2.113848416.1 x6 - 3x5 + 2x4 - 10x3 + 36x2 - 48x + 24 \( 2^{5}\cdot 3^{5}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.0.118987407.1 x6 - x5 + 19x4 + 3x3 + 84x2 + 162x + 81 \( -\,3^{3}\cdot 7\cdot 11^{4}\cdot 43 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.122984400.1 x6 - x5 + 6x4 - 3x3 + 4x2 - 9x - 27 \( 2^{4}\cdot 3\cdot 5^{2}\cdot 7\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.2.151797888.1 x6 - 2x5 + 3x4 - 18x3 - 24x2 - 18x - 6 \( 2^{7}\cdot 3^{4}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.0.158357056.3 x6 - 2x5 - 13x4 + 18x3 + 166x2 - 270x + 125 \( -\,2^{6}\cdot 11^{4}\cdot 13^{2} \) $S_3\times C_3$ (as 6T5) $[3]$
6.0.158357056.4 x6 - 2x5 - 20x4 - 2x3 + 163x2 + 328x + 241 \( -\,2^{6}\cdot 11^{4}\cdot 13^{2} \) $S_3\times C_3$ (as 6T5) $[3]$
6.0.170772624.1 x6 - 3x5 - 18x4 + 19x3 + 126x2 + 117x + 31 \( -\,2^{4}\cdot 3^{6}\cdot 11^{4} \) $C_3^2:D_4$ (as 6T13) trivial
6.4.176160512.1 x6 - x5 - 3x4 + 14x3 - 37x2 + 19x + 15 \( -\,2^{8}\cdot 11^{4}\cdot 47 \) $S_6$ (as 6T16) trivial
6.2.202397184.1 x6 - 13x4 - 22x3 - 6x2 - 6 \( 2^{9}\cdot 3^{3}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.4.209893376.1 x6 - 2x5 + x4 - 8x3 - 27x2 - 6x + 7 \( -\,2^{11}\cdot 7\cdot 11^{4} \) $C_3^2:D_4$ (as 6T13) trivial
6.4.227696832.1 x6 - 13x4 + 27x2 - 22x + 5 \( -\,2^{6}\cdot 3^{5}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.4.239878144.1 x6 - 8x4 - 44x3 + 69x2 + 132x + 34 \( -\,2^{14}\cdot 11^{4} \) $C_3^2:D_4$ (as 6T13) trivial
6.2.247842848.1 x6 - 2x5 + 3x4 - 40x3 + 108x2 - 84x + 16 \( 2^{5}\cdot 11^{4}\cdot 23^{2} \) $S_6$ (as 6T16) trivial
6.0.264460383.1 x6 - 2x5 - 24x4 + 7x3 + 265x2 + 588x + 444 \( -\,3^{4}\cdot 11^{4}\cdot 223 \) $C_3^2:D_4$ (as 6T13) $[2]$
6.2.275485056.1 x6 - 2x5 - 4x4 + 6x3 + x2 + 48x - 126 \( 2^{7}\cdot 3\cdot 7^{2}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.0.288178803.2 x6 - 11x3 + 121 \( -\,3^{9}\cdot 11^{4} \) $S_3\times C_3$ (as 6T5) trivial
6.0.292922487.1 x6 - x5 - 25x4 + 47x3 + 161x2 - 520x + 400 \( -\,3^{4}\cdot 11^{4}\cdot 13\cdot 19 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.293288512.1 x6 - 2x5 + 2x4 - 2x3 + 31x2 + 42x + 65 \( -\,2^{6}\cdot 11^{4}\cdot 313 \) $C_3^2:D_4$ (as 6T13) $[3]$
6.0.299247399.1 x6 - x5 + 19x4 - 19x3 + 95x2 - 36x + 4 \( -\,3^{3}\cdot 11^{4}\cdot 757 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.309920688.4 x6 + x4 - 22x3 - 95x2 + 22x + 889 \( -\,2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 11^{4} \) $S_3\times C_3$ (as 6T5) $[3]$
6.0.322965819.1 x6 + 22x4 - 44x3 + 121x2 - 484x + 847 \( -\,3^{3}\cdot 11^{4}\cdot 19\cdot 43 \) $C_3^2:D_4$ (as 6T13) $[2]$
6.4.330871959.1 x6 - 6x4 - 11x3 + 12x2 + 33x + 14 \( -\,3^{6}\cdot 11^{4}\cdot 31 \) $S_6$ (as 6T16) trivial
6.2.341545248.4 x6 + 9x4 - 6x2 - 66x + 60 \( 2^{5}\cdot 3^{6}\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.2.345893625.3 x6 - x5 - x4 - 13x3 - 24x2 - 15x - 3 \( 3^{3}\cdot 5^{3}\cdot 7\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.0.351427923.1 x6 - 2x5 - 24x4 + 62x3 + 210x2 - 644x + 433 \( -\,3^{3}\cdot 7\cdot 11^{4}\cdot 127 \) $C_3^2:D_4$ (as 6T13) trivial
6.6.352569921.1 x6 - x5 - 13x4 - 5x3 + 26x2 + 18x + 3 \( 3\cdot 11^{4}\cdot 23\cdot 349 \) $S_6$ (as 6T16) trivial
6.0.363565312.1 x6 - 2x5 + 2x4 - 68x3 + 108x2 + 64x + 692 \( -\,2^{8}\cdot 11^{4}\cdot 97 \) $C_3^2:D_4$ (as 6T13) $[3]$
6.6.367313408.1 x6 - 2x5 - 21x4 + 14x3 + 72x2 - 72x + 7 \( 2^{9}\cdot 7^{2}\cdot 11^{4} \) $S_3\times C_3$ (as 6T5) trivial
6.0.374809600.2 x6 - 2x5 + 9x4 - 48x3 + 177x2 - 402x + 521 \( -\,2^{10}\cdot 5^{2}\cdot 11^{4} \) $S_3^2$ (as 6T9) $[3]$
6.0.379890027.1 x6 - x5 + 41x4 - 30x3 + 480x2 - 344x + 1456 \( -\,3^{3}\cdot 11^{4}\cdot 31^{2} \) $S_3\times C_3$ (as 6T5) trivial
6.0.393784336.1 x6 - x5 + 3x4 - 23x3 + 32x2 + 6x + 2 \( -\,2^{4}\cdot 11^{4}\cdot 41^{2} \) $S_6$ (as 6T16) trivial
6.2.398469456.1 x6 - x5 - 2x4 - 16x3 + 48x2 - 48x - 96 \( 2^{4}\cdot 3^{5}\cdot 7\cdot 11^{4} \) $S_6$ (as 6T16) trivial
6.0.417839499.1 x6 - x5 - 25x4 - 8x3 + 205x2 + 129x + 147 \( -\,3^{3}\cdot 7\cdot 11^{4}\cdot 151 \) $C_3^2:D_4$ (as 6T13) trivial
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