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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 6.0.9747.1 | x6 - x5 + x4 - 2x3 + 4x2 - 3x + 1 | \( -\,3^{3}\cdot 19^{2} \) | $S_3\times C_3$ (as 6T5) | Trivial |
| 6.0.10051.1 | x6 - x5 + 2x4 - 2x3 + 2x2 - 2x + 1 | \( -\,19\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.10571.1 | x6 - x5 - x4 + 2x3 - x + 1 | \( -\,11\cdot 31^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.10816.1 | x6 - x4 - 2x3 + 2x + 1 | \( -\,2^{6}\cdot 13^{2} \) | $S_3\times C_3$ (as 6T5) | Trivial |
| 6.0.11691.1 | x6 - x5 - x2 + x + 1 | \( -\,3^{3}\cdot 433 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.12167.1 | x6 - 3x5 + 5x4 - 5x3 + 5x2 - 3x + 1 | \( -\,23^{3} \) | $S_3$ (as 6T2) | Trivial |
| 6.0.14283.1 | x6 - x5 + x4 - 2x3 + x2 + 1 | \( -\,3^{3}\cdot 23^{2} \) | $D_{6}$ (as 6T3) | Trivial |
| 6.0.14731.1 | x6 - x5 + x3 - x2 + 1 | \( -\,14731 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.16551.1 | x6 - x5 - x4 + 3x3 - 2x + 1 | \( -\,3^{3}\cdot 613 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.16807.1 | x6 - x5 + x4 - x3 + x2 - x + 1 | \( -\,7^{5} \) | $C_6$ (as 6T1) | Trivial |
| 6.0.18515.1 | x6 + 2x4 - x3 + 2x2 + 1 | \( -\,5\cdot 7\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.19683.1 | x6 - x3 + 1 | \( -\,3^{9} \) | $C_6$ (as 6T1) | Trivial |
| 6.0.20627.1 | x6 - x5 + x4 - 2x3 + 2x2 - x + 1 | \( -\,20627 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.21168.1 | x6 - 3x5 + 4x4 - x3 - 2x2 + x + 1 | \( -\,2^{4}\cdot 3^{3}\cdot 7^{2} \) | $S_3\times C_3$ (as 6T5) | Trivial |
| 6.0.21296.1 | x6 - x5 + 2x4 - 3x3 + 2x2 - x + 1 | \( -\,2^{4}\cdot 11^{3} \) | $S_3$ (as 6T2) | Trivial |
| 6.0.22291.1 | x6 + x4 - x3 - x + 1 | \( -\,22291 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.22592.1 | x6 - 2x5 + 2x4 - x2 + 1 | \( -\,2^{6}\cdot 353 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.22707.1 | x6 - x5 + 4x4 - 4x3 + 5x2 - 3x + 1 | \( -\,3^{3}\cdot 29^{2} \) | $D_{6}$ (as 6T3) | Trivial |
| 6.0.22747.1 | x6 - x5 - 2x3 + x2 + x + 1 | \( -\,23^{2}\cdot 43 \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.23031.1 | x6 + x4 - x3 + x2 - 2x + 1 | \( -\,3^{3}\cdot 853 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.24003.1 | x6 - x5 + 3x3 - x2 - 2x + 1 | \( -\,3^{3}\cdot 7\cdot 127 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.25747.1 | x6 - x5 + 2x4 - 2x3 + 3x2 - x + 1 | \( -\,25747 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.25947.1 | x6 - x4 - 2x3 + x2 + x + 1 | \( -\,3^{3}\cdot 31^{2} \) | $D_{6}$ (as 6T3) | Trivial |
| 6.0.27556.1 | x6 - x5 + 2x3 - x + 1 | \( -\,2^{2}\cdot 83^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.27848.1 | x6 - x5 + 2x4 + 2x2 - x + 1 | \( -\,2^{3}\cdot 59^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.27971.1 | x6 - x5 + x4 - 2x3 + 3x2 - 2x + 1 | \( -\,83\cdot 337 \) | $S_6$ (as 6T16) | Trivial |
| 6.2.28037.1 | x6 - 2x5 + 3x3 - 2x - 1 | \( 23^{2}\cdot 53 \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.2.29077.1 | x6 - x5 + x4 - x2 + 2x - 1 | \( 29077 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.29095.1 | x6 - x5 + 3x4 - x3 + 3x2 - x + 1 | \( -\,5\cdot 11\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.2.29189.1 | x6 - 2x5 + x4 + x3 - 2x2 + x + 1 | \( 17^{2}\cdot 101 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.29791.1 | x6 - 3x5 + 7x4 - 9x3 + 7x2 - 3x + 1 | \( -\,31^{3} \) | $S_3$ (as 6T2) | Trivial |
| 6.2.30125.1 | x6 - x5 + x4 - 2x2 + x - 1 | \( 5^{3}\cdot 241 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.30808.1 | x6 - x4 - x3 + x2 + x + 1 | \( -\,2^{3}\cdot 3851 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.30976.1 | x6 - 2x5 + 2x4 - 2x3 + 4x2 - 4x + 2 | \( -\,2^{8}\cdot 11^{2} \) | $D_{6}$ (as 6T3) | Trivial |
| 6.2.31133.1 | x6 - 2x4 - x3 + 2x + 1 | \( 163\cdot 191 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.31211.1 | x6 - x4 - x3 + 2x2 + 3x + 1 | \( -\,23^{2}\cdot 59 \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.2.31213.1 | x6 - 2x5 + 2x4 - 3x3 + 2x2 - 2x + 1 | \( 7^{4}\cdot 13 \) | $A_4\times C_2$ (as 6T6) | Trivial |
| 6.0.31223.1 | x6 - x5 + x4 - x3 + 2x2 - x + 1 | \( -\,31223 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.31347.1 | x6 - 3x4 - 2x3 + 3x2 + 3x + 1 | \( -\,3^{6}\cdot 43 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.2.31709.1 | x6 - x5 + 2x3 - 2x2 + 1 | \( 37\cdot 857 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.32171.1 | x6 - x5 + 2x4 - x3 + x2 + 1 | \( -\,53\cdot 607 \) | $S_6$ (as 6T16) | Trivial |
| 6.2.32269.1 | x6 - 3x5 + 4x4 - 3x3 + x2 - 1 | \( 23^{2}\cdot 61 \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.32911.1 | x6 - x3 - x2 + x + 1 | \( -\,32911 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.33791.1 | x6 - x5 + x4 + x3 + x + 1 | \( -\,33791 \) | $S_6$ (as 6T16) | Trivial |
| 6.0.33856.1 | x6 - x4 + 1 | \( -\,2^{6}\cdot 23^{2} \) | $S_4\times C_2$ (as 6T11) | Trivial |
| 6.0.33856.2 | x6 + x4 + 2x2 + 1 | \( -\,2^{6}\cdot 23^{2} \) | $D_{6}$ (as 6T3) | Trivial |
| 6.2.33856.1 | x6 + x4 - 1 | \( 2^{6}\cdot 23^{2} \) | $S_4$ (as 6T7) | Trivial |
| 6.0.34371.1 | x6 - x5 - 2x3 + 2x + 1 | \( -\,3^{3}\cdot 19\cdot 67 \) | $C_3^2:D_4$ (as 6T13) | Trivial |
| 6.0.34992.1 | x6 - 3x5 + 5x3 - 3x + 1 | \( -\,2^{4}\cdot 3^{7} \) | $S_3$ (as 6T2) | Trivial |
| 6.0.35099.1 | x6 + x4 + x2 - x + 1 | \( -\,35099 \) | $S_6$ (as 6T16) | Trivial |
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