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Label Polynomial Discriminant Galois group Class group
6.2.266944.1 x6 - 2x5 + 2x3 + 3x2 - 4x + 1 \( 2^{6}\cdot 43\cdot 97 \) $S_6$ (as 6T16) trivial
6.4.288576.1 x6 - 2x5 - x2 + 2x + 1 \( -\,2^{6}\cdot 3^{3}\cdot 167 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.392000.1 x6 - 2x5 + 3x4 + 4x2 + 2x + 1 \( -\,2^{6}\cdot 5^{3}\cdot 7^{2} \) $S_3\times C_3$ (as 6T5) $[2]$
6.2.430272.1 x6 - 2x5 + 2x4 - 2x3 - x2 - 2x + 1 \( 2^{6}\cdot 3^{4}\cdot 83 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.479936.1 x6 + x4 + 2x2 - 4x + 1 \( 2^{6}\cdot 7499 \) $S_6$ (as 6T16) trivial
6.4.483136.1 x6 - 2x5 - x4 + 4x3 - 4x2 + 2x + 1 \( -\,2^{6}\cdot 7549 \) $S_6$ (as 6T16) trivial
6.2.489152.1 x6 + 3x4 - 2x3 - 2x + 1 \( 2^{6}\cdot 7643 \) $S_6$ (as 6T16) trivial
6.2.513216.1 x6 - 2x3 - 3x2 + 1 \( 2^{6}\cdot 3^{6}\cdot 11 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.540864.2 x6 - 2x5 + x4 + 4x3 - 4x2 + 1 \( 2^{6}\cdot 3^{3}\cdot 313 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.543424.1 x6 - 2x5 + 4x3 - 5x2 + 2x + 1 \( 2^{6}\cdot 7\cdot 1213 \) $S_6$ (as 6T16) trivial
6.2.576704.1 x6 - 2x4 - 4x3 - 3x2 + 1 \( 2^{6}\cdot 9011 \) $S_6$ (as 6T16) trivial
6.2.578752.1 x6 - 2x5 + 4x4 - 2x3 - x2 + 4x - 3 \( 2^{6}\cdot 9043 \) $S_6$ (as 6T16) trivial
6.2.643264.1 x6 + 2x4 - 7x2 - 19 \( 2^{6}\cdot 19\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.0.648000.1 x6 - 2x5 + 2x4 - 4x3 + 7x2 - 4x + 1 \( -\,2^{6}\cdot 3^{4}\cdot 5^{3} \) $S_3\times C_3$ (as 6T5) $[2]$
6.2.676544.2 x6 - 6x4 + 13x2 - 11 \( 2^{6}\cdot 11\cdot 31^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.2.686784.1 x6 - 2x5 + 3x4 - 4x2 + 6x - 3 \( 2^{6}\cdot 3\cdot 7^{2}\cdot 73 \) $S_6$ (as 6T16) trivial
6.2.696512.1 x6 - 3x4 - 6x3 - 4x2 + 1 \( 2^{6}\cdot 10883 \) $S_6$ (as 6T16) trivial
6.2.742592.1 x6 - 2x5 + x4 + 4x3 - 8x2 + 8x - 3 \( 2^{6}\cdot 41\cdot 283 \) $S_6$ (as 6T16) trivial
6.4.744768.1 x6 - x4 - 4x3 - 2x2 + 2x + 1 \( -\,2^{6}\cdot 3^{3}\cdot 431 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.831168.1 x6 + x4 - 2x3 + 4x2 - 4x + 1 \( 2^{6}\cdot 3^{3}\cdot 13\cdot 37 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.914112.1 x6 - 3x4 + 18x2 - 27 \( 2^{6}\cdot 3^{3}\cdot 23^{2} \) $D_{6}$ (as 6T3) trivial
6.0.954176.1 x6 - 2x5 + 3x4 - 4x3 + 2x + 1 \( -\,2^{6}\cdot 17\cdot 877 \) $S_6$ (as 6T16) $[2]$
6.2.997056.1 x6 - 2x5 + 2x3 + 3x2 + 4x + 1 \( 2^{6}\cdot 3^{3}\cdot 577 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.1019712.1 x6 - 2x5 + 3x4 - 6x3 + 6x2 - 2x + 1 \( -\,2^{6}\cdot 3\cdot 47\cdot 113 \) $S_6$ (as 6T16) $[2]$
6.2.1023680.2 x6 - 2x5 + 2x4 + 2x3 - x2 + 2x + 1 \( 2^{6}\cdot 5\cdot 7\cdot 457 \) $S_6$ (as 6T16) trivial
6.2.1042624.1 x6 - x4 - 2x2 - 2x + 1 \( 2^{6}\cdot 11\cdot 1481 \) $S_6$ (as 6T16) trivial
6.2.1121472.1 x6 - 2x5 + 2x4 + 2x3 - 5x2 + 6x - 3 \( 2^{6}\cdot 3^{3}\cdot 11\cdot 59 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.1174336.1 x6 - 3x4 + 6x2 - 4x + 1 \( -\,2^{6}\cdot 59\cdot 311 \) $S_6$ (as 6T16) $[2]$
6.2.1184960.2 x6 - 6x4 + 17x2 - 35 \( 2^{6}\cdot 5\cdot 7\cdot 23^{2} \) $S_4\times C_2$ (as 6T11) trivial
6.4.1195328.1 x6 - 2x5 + x4 - 4x2 + 1 \( -\,2^{6}\cdot 19\cdot 983 \) $S_6$ (as 6T16) trivial
6.2.1198784.2 x6 - 4x4 + 9x2 - 6x + 1 \( 2^{6}\cdot 18731 \) $S_6$ (as 6T16) trivial
6.2.1230016.1 x6 + x4 - 6x2 - 4x + 1 \( 2^{6}\cdot 19219 \) $S_6$ (as 6T16) trivial
6.6.1259712.1 x6 - 6x4 + 9x2 - 3 \( 2^{6}\cdot 3^{9} \) $C_6$ (as 6T1) trivial
6.2.1287360.1 x6 - 2x5 + 5x4 - 4x3 + 4x2 - 4x + 1 \( 2^{6}\cdot 3^{3}\cdot 5\cdot 149 \) $S_6$ (as 6T16) trivial
6.2.1311936.1 x6 - 2x5 + 3x4 - 2x3 - 2x2 + 2x - 3 \( 2^{6}\cdot 3\cdot 6833 \) $S_6$ (as 6T16) trivial
6.2.1313984.1 x6 - 3x4 - 2x3 + 4x2 + 1 \( 2^{6}\cdot 7^{2}\cdot 419 \) $S_6$ (as 6T16) trivial
6.0.1317184.1 x6 + 5x2 - 2x + 1 \( -\,2^{6}\cdot 11\cdot 1871 \) $S_6$ (as 6T16) $[2]$
6.4.1325376.1 x6 - 2x4 - 4x3 + x2 + 4x + 1 \( -\,2^{6}\cdot 3^{3}\cdot 13\cdot 59 \) $C_3^2:D_4$ (as 6T13) trivial
6.2.1355456.1 x6 - 2x3 + x2 - 4x + 1 \( 2^{6}\cdot 21179 \) $S_6$ (as 6T16) trivial
6.2.1378496.1 x6 - 2x5 + x4 - 4x + 1 \( 2^{6}\cdot 7\cdot 17\cdot 181 \) $S_6$ (as 6T16) trivial
6.2.1395904.2 x6 - 2x5 - x4 + 8x2 - 6x + 1 \( 2^{6}\cdot 17\cdot 1283 \) $S_6$ (as 6T16) trivial
6.2.1406656.1 x6 - 2x5 + 2x4 + 2x3 - 5x2 - 2x + 1 \( 2^{6}\cdot 31\cdot 709 \) $S_6$ (as 6T16) trivial
6.2.1453248.1 x6 + x4 - 2x2 - 3 \( 2^{6}\cdot 3^{3}\cdot 29^{2} \) $D_{6}$ (as 6T3) trivial
6.2.1453248.5 x6 - 2x5 + 2x4 + 3x2 - 4x + 1 \( 2^{6}\cdot 3^{3}\cdot 29^{2} \) $S_3^2$ (as 6T9) trivial
6.2.1455808.1 x6 + x4 + 6x2 - 43 \( 2^{6}\cdot 23^{2}\cdot 43 \) $S_4\times C_2$ (as 6T11) trivial
6.2.1509568.1 x6 - 2x5 + 6x3 - 5x2 + 1 \( 2^{6}\cdot 103\cdot 229 \) $S_6$ (as 6T16) trivial
6.2.1519808.1 x6 - x4 - 4x3 - 2x2 - 2x + 1 \( 2^{6}\cdot 23747 \) $S_6$ (as 6T16) trivial
6.2.1550016.1 x6 - 2x5 + 4x4 - 6x3 + 3x2 - 3 \( 2^{6}\cdot 3^{4}\cdot 13\cdot 23 \) $C_3^2:D_4$ (as 6T13) trivial
6.0.1641792.1 x6 + 3x4 - 2x3 + 4x2 + 2x + 1 \( -\,2^{6}\cdot 3\cdot 17\cdot 503 \) $S_6$ (as 6T16) $[2]$
6.2.1660608.1 x6 + 6x4 + 9x2 - 27 \( 2^{6}\cdot 3^{3}\cdot 31^{2} \) $D_{6}$ (as 6T3) trivial
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