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Label Polynomial Discriminant Galois group Class group
6.0.9747.1 x6 - x5 + x4 - 2x3 + 4x2 - 3x + 1 \( -\,3^{3}\cdot 19^{2} \) $S_3\times C_3$ Trivial
6.0.10816.1 x6 - x4 - 2x3 + 2x + 1 \( -\,2^{6}\cdot 13^{2} \) $S_3\times C_3$ Trivial
6.0.21168.1 x6 - 3x5 + 4x4 - x3 - 2x2 + x + 1 \( -\,2^{4}\cdot 3^{3}\cdot 7^{2} \) $S_3\times C_3$ Trivial
6.0.36963.1 x6 - 3x5 + 4x4 - 2x3 - 2x2 + 2x + 1 \( -\,3^{3}\cdot 37^{2} \) $S_3\times C_3$ Trivial
6.0.41472.1 x6 - 2x5 + 3x4 - 2x3 + 2x2 + 1 \( -\,2^{9}\cdot 3^{4} \) $S_3\times C_3$ Trivial
6.0.73008.1 x6 - x5 - 4x4 + 3x3 + 6x2 - 5x + 1 \( -\,2^{4}\cdot 3^{3}\cdot 13^{2} \) $S_3\times C_3$ Trivial
6.0.87616.1 x6 - 2x5 - 2x4 + 4x3 + 3x2 - 4x + 1 \( -\,2^{6}\cdot 37^{2} \) $S_3\times C_3$ Trivial
6.0.107163.1 x6 - x3 + 7 \( -\,3^{7}\cdot 7^{2} \) $S_3\times C_3$ Trivial
6.0.107811.1 x6 - x4 - 2x3 + 3x2 + x + 1 \( -\,3^{4}\cdot 11^{3} \) $S_3\times C_3$ Trivial
6.0.143883.1 x6 - 3x5 + 4x4 - 2x2 + 3 \( -\,3^{3}\cdot 73^{2} \) $S_3\times C_3$ Trivial
6.0.177147.1 x6 - 3x3 + 3 \( -\,3^{11} \) $S_3\times C_3$ Trivial
6.0.184832.1 x6 - 2x5 + x4 + 2x3 - 4x + 3 \( -\,2^{9}\cdot 19^{2} \) $S_3\times C_3$ Trivial
6.0.223587.1 x6 - 3x5 + 4x4 - 5x2 + 3x + 3 \( -\,3^{3}\cdot 7^{2}\cdot 13^{2} \) $S_3\times C_3$ Trivial
6.0.223587.2 x6 + x4 - 2x3 - 5x2 + 2x + 4 \( -\,3^{3}\cdot 7^{2}\cdot 13^{2} \) $S_3\times C_3$ Trivial
6.0.238144.2 x6 - 2x5 + 5x4 - 8x3 + 12x2 - 12x + 5 \( -\,2^{6}\cdot 61^{2} \) $S_3\times C_3$ Trivial
6.0.314928.1 x6 - 2x3 + 4 \( -\,2^{4}\cdot 3^{9} \) $S_3\times C_3$ Trivial
6.0.320787.3 x6 - 3x5 + 4x4 + x3 - 5x2 + 2x + 4 \( -\,3^{3}\cdot 109^{2} \) $S_3\times C_3$ Trivial
6.0.336091.1 x6 - x5 + x4 + 5x2 + 4x + 1 \( -\,7^{2}\cdot 19^{3} \) $S_3\times C_3$ Trivial
6.0.341056.1 x6 - 5x4 + 10x2 - 6x + 1 \( -\,2^{6}\cdot 73^{2} \) $S_3\times C_3$ Trivial
6.0.369603.2 x6 - 5x3 + 13 \( -\,3^{7}\cdot 13^{2} \) $S_3\times C_3$ Trivial
6.0.392000.1 x6 - 2x5 + 3x4 + 4x2 + 2x + 1 \( -\,2^{6}\cdot 5^{3}\cdot 7^{2} \) $S_3\times C_3$ $[2]$
6.0.415152.1 x6 - x5 + 8x4 - 3x3 + 18x2 + x + 13 \( -\,2^{4}\cdot 3^{3}\cdot 31^{2} \) $S_3\times C_3$ Trivial
6.0.419904.3 x6 - 2x3 + 9x2 - 12x + 5 \( -\,2^{6}\cdot 3^{8} \) $S_3\times C_3$ Trivial
6.0.435483.1 x6 - 3x5 + 4x4 - x3 - 5x2 + 4x + 4 \( -\,3^{3}\cdot 127^{2} \) $S_3\times C_3$ Trivial
6.0.469567.1 x6 - x5 + 3x4 + 2x3 + 6x2 + 3x + 2 \( -\,7^{3}\cdot 37^{2} \) $S_3\times C_3$ Trivial
6.0.602176.1 x6 - 2x5 - 4x4 + 11x2 + 14x + 5 \( -\,2^{6}\cdot 97^{2} \) $S_3\times C_3$ Trivial
6.0.634207.1 x6 - x5 - 3x4 + x3 + 7x2 - 5x + 1 \( -\,7^{3}\cdot 43^{2} \) $S_3\times C_3$ Trivial
6.0.648000.1 x6 - 2x5 + 2x4 - 4x3 + 7x2 - 4x + 1 \( -\,2^{6}\cdot 3^{4}\cdot 5^{3} \) $S_3\times C_3$ $[2]$
6.0.677376.1 x6 - 2x5 + 3x4 - 6x3 + 8x2 - 4x + 1 \( -\,2^{9}\cdot 3^{3}\cdot 7^{2} \) $S_3\times C_3$ $[2]$
6.0.717363.1 x6 + x4 - x3 - 8x2 + x + 7 \( -\,3^{3}\cdot 163^{2} \) $S_3\times C_3$ Trivial
6.6.722000.1 x6 - x5 - 6x4 + 7x3 + 4x2 - 5x + 1 \( 2^{4}\cdot 5^{3}\cdot 19^{2} \) $S_3\times C_3$ Trivial
6.0.760384.2 x6 - 2x5 - 5x4 + 14x3 + 2x2 - 24x + 16 \( -\,2^{6}\cdot 109^{2} \) $S_3\times C_3$ Trivial
6.0.798768.2 x6 - 3x5 + 4x4 + x3 - 2x2 - x + 7 \( -\,2^{4}\cdot 3^{3}\cdot 43^{2} \) $S_3\times C_3$ Trivial
6.0.826875.2 x6 - x5 + 9x4 - 6x3 + 26x2 - 11x + 19 \( -\,3^{3}\cdot 5^{4}\cdot 7^{2} \) $S_3\times C_3$ Trivial
6.0.884547.1 x6 - 3x5 + 4x4 + 2x3 - 5x2 + x + 7 \( -\,3^{3}\cdot 181^{2} \) $S_3\times C_3$ Trivial
6.0.946688.1 x6 + 4x4 + 3x2 - 4x + 4 \( -\,2^{9}\cdot 43^{2} \) $S_3\times C_3$ Trivial
6.0.964467.2 x6 - 5x3 + 7 \( -\,3^{9}\cdot 7^{2} \) $S_3\times C_3$ Trivial
6.0.964467.3 x6 - 4x3 + 7 \( -\,3^{9}\cdot 7^{2} \) $S_3\times C_3$ Trivial
6.0.1069227.2 x6 - 3x5 + 4x4 + 2x3 - 8x2 + 4x + 7 \( -\,3^{3}\cdot 199^{2} \) $S_3\times C_3$ Trivial
6.0.1218375.1 x6 - x5 + 3x4 - 6x3 + 11x2 - 8x + 4 \( -\,3^{3}\cdot 5^{3}\cdot 19^{2} \) $S_3\times C_3$ $[2]$
6.0.1271403.1 x6 - 3x5 + 4x4 - 2x3 - 5x2 + 5x + 7 \( -\,3^{3}\cdot 7^{2}\cdot 31^{2} \) $S_3\times C_3$ Trivial
6.0.1271403.2 x6 + x4 - 3x3 - 8x2 + 3x + 9 \( -\,3^{3}\cdot 7^{2}\cdot 31^{2} \) $S_3\times C_3$ Trivial
6.0.1279091.2 x6 - 2x5 - 2x3 + 6x2 - 4x + 5 \( -\,11^{3}\cdot 31^{2} \) $S_3\times C_3$ Trivial
6.0.1539727.1 x6 - 3x5 + 3x4 + x3 + x2 - 5x + 11 \( -\,7^{3}\cdot 67^{2} \) $S_3\times C_3$ Trivial
6.0.1577536.1 x6 - 2x5 - 2x4 + 6x3 + 17x2 + 8x + 4 \( -\,2^{6}\cdot 157^{2} \) $S_3\times C_3$ Trivial
6.0.1607472.1 x6 - 3x5 + 4x4 + 3x3 - 8x2 + 3x + 9 \( -\,2^{4}\cdot 3^{3}\cdot 61^{2} \) $S_3\times C_3$ Trivial
6.0.1714608.2 x6 - 3x5 - 6x4 + 13x3 + 24x2 + 9x + 1 \( -\,2^{4}\cdot 3^{7}\cdot 7^{2} \) $S_3\times C_3$ $[3]$
6.0.1724976.1 x6 - x5 - 2x4 - x3 + 8x2 - 5x + 1 \( -\,2^{4}\cdot 3^{4}\cdot 11^{3} \) $S_3\times C_3$ $[3]$
6.0.1724976.2 x6 - x5 - 2x4 + 3x3 + 6x2 - 15x + 9 \( -\,2^{4}\cdot 3^{4}\cdot 11^{3} \) $S_3\times C_3$ $[3]$
6.0.1822139.1 x6 - 3x5 + 7x4 - 4x3 + 8x2 - x + 3 \( -\,11^{3}\cdot 37^{2} \) $S_3\times C_3$ Trivial

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