| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.18.24.10 |
$18$ |
$x^{18} + 6 x^{17} + 8 x^{16} - 2 x^{15} + 14 x^{14} + 24 x^{13} + 18 x^{12} + 120 x^{11} + 64 x^{10} + 24 x^{9} + 232 x^{8} - 16 x^{7} + 228 x^{6} + 264 x^{5} - 48 x^{4} + 216 x^{3} + 72 x^{2} + 216$ |
$2$ |
$6$ |
$3$ |
$24$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[2]$ |
$[2]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t^{2} x^{4} + 2 x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 6$ |
$[3, 0]$ |
$[1, 2]$ |
| 2.18.24.30 |
$18$ |
$x^{18} + 6 x^{16} + 18 x^{15} + 2 x^{14} + 36 x^{13} + 94 x^{12} + 128 x^{11} + 112 x^{10} + 32 x^{9} + 256 x^{8} + 184 x^{7} + 292 x^{6} - 16 x^{5} + 248 x^{4} + 120 x^{3} + 216 x^{2} + 72$ |
$2$ |
$6$ |
$3$ |
$24$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[2]$ |
$[2]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{4} + 2 x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 2]$ |
| 2.18.33.58 |
$18$ |
$x^{18} - 8 x^{17} + 22 x^{16} + 92 x^{15} - 58 x^{14} + 172 x^{13} + 374 x^{12} + 272 x^{11} + 444 x^{10} + 816 x^{9} + 712 x^{8} + 1024 x^{7} + 980 x^{6} + 784 x^{5} + 560 x^{4} + 272 x^{3} + 136 x^{2} + 48 x + 8$ |
$2$ |
$6$ |
$3$ |
$33$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[3]$ |
$[3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + 4 t^{2} x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + 4 x + 2$ |
$[6, 0]$ |
$[1, 2]$ |
| 2.18.33.159 |
$18$ |
$x^{18} - 8 x^{17} + 80 x^{16} + 48 x^{15} - 182 x^{14} - 492 x^{13} - 746 x^{12} - 176 x^{11} + 152 x^{10} - 376 x^{9} + 464 x^{8} + 560 x^{7} + 3204 x^{6} + 4224 x^{5} + 3360 x^{4} + 3824 x^{3} + 2536 x^{2} + 4080 x + 3624$ |
$2$ |
$6$ |
$3$ |
$33$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[3]$ |
$[3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + \left(4 t^{2} + 4 t\right) x^{5} + 6 t x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(2 t + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 8 t + 10$ |
$[6, 0]$ |
$[1, 2]$ |
| 2.18.33.308 |
$18$ |
$x^{18} + 8 x^{16} - 8 x^{15} + 28 x^{14} - 176 x^{13} - 182 x^{12} - 128 x^{11} - 684 x^{10} - 536 x^{9} - 24 x^{8} + 544 x^{7} + 404 x^{6} + 1904 x^{5} + 3768 x^{4} + 3152 x^{3} + 1072 x^{2} + 3424 x + 6392$ |
$2$ |
$6$ |
$3$ |
$33$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[3]$ |
$[3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + 4 t x^{5} + \left(4 t^{2} + 2 t\right) x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 2 t x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 12 t + 14$ |
$[6, 0]$ |
$[1, 2]$ |
| 2.18.33.309 |
$18$ |
$x^{18} + 4 x^{17} + 6 x^{16} + 84 x^{15} + 24 x^{14} + 304 x^{13} + 190 x^{12} + 480 x^{11} + 1096 x^{10} + 640 x^{9} + 1912 x^{8} + 1312 x^{7} + 1340 x^{6} + 3408 x^{5} + 1016 x^{4} + 2480 x^{3} + 1488 x^{2} + 2728$ |
$2$ |
$6$ |
$3$ |
$33$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[3]$ |
$[3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{6} + \left(4 t^{2} + 4\right) x^{5} + 2 x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 12 t^{2} + 4 t + 10$ |
$[6, 0]$ |
$[1, 2]$ |
| 5.18.15.1 |
$18$ |
$x^{18} + 18 x^{16} + 18 x^{15} + 135 x^{14} + 270 x^{13} + 690 x^{12} + 1620 x^{11} + 2475 x^{10} + 3150 x^{9} + 10773 x^{8} + 16200 x^{7} + 38064 x^{6} + 9234 x^{5} + 34200 x^{4} - 11862 x^{3} + 43200 x^{2} - 19386 x + 12329$ |
$5$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{6} + 5$ |
$[0]$ |
$[2]$ |
| 5.18.15.2 |
$18$ |
$x^{18} + 75 x^{6} - 375$ |
$5$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{6} + 5 t$ |
$[0]$ |
$[2]$ |
| 11.18.15.1 |
$18$ |
$x^{18} + 242 x^{6} - 11979$ |
$11$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 9$ |
$x^{6} + 11 t$ |
$[0]$ |
$[2]$ |
| 11.18.15.2 |
$18$ |
$x^{18} + 12 x^{16} + 54 x^{15} + 60 x^{14} + 540 x^{13} + 1408 x^{12} + 2160 x^{11} + 9432 x^{10} + 4050 x^{9} + 31332 x^{8} + 109620 x^{7} + 516199 x^{6} + 148176 x^{5} + 568860 x^{4} - 690336 x^{3} + 570672 x^{2} + 248832 x + 820224$ |
$11$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 9$ |
$x^{6} + 11$ |
$[0]$ |
$[2]$ |
| 17.18.15.1 |
$18$ |
$x^{18} + 6 x^{16} + 84 x^{15} + 15 x^{14} + 420 x^{13} + 3011 x^{12} + 840 x^{11} + 11367 x^{10} + 20020 x^{9} + 18411 x^{8} + 186480 x^{7} + 1998610 x^{6} + 147588 x^{5} + 1446885 x^{4} - 3479756 x^{3} + 734952 x^{2} + 1984584 x + 9683028$ |
$17$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + t + 14$ |
$x^{6} + 17$ |
$[0]$ |
$[2]$ |
| 17.18.15.2 |
$18$ |
$x^{18} + 289 x^{6} - 68782$ |
$17$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + t + 14$ |
$x^{6} + 17 t$ |
$[0]$ |
$[2]$ |
| 23.18.15.1 |
$18$ |
$x^{18} + 1058 x^{6} - 219006$ |
$23$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 18$ |
$x^{6} + 23 t$ |
$[0]$ |
$[2]$ |
| 23.18.15.2 |
$18$ |
$x^{18} + 12 x^{16} + 108 x^{15} + 60 x^{14} + 1080 x^{13} + 5089 x^{12} + 4320 x^{11} + 38016 x^{10} + 63180 x^{9} + 120972 x^{8} + 783000 x^{7} + 4887319 x^{6} + 1283904 x^{5} + 7691460 x^{4} - 7377912 x^{3} + 7707816 x^{2} + 15625224 x + 42132627$ |
$23$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 18$ |
$x^{6} + 23$ |
$[0]$ |
$[2]$ |
| 29.18.15.1 |
$18$ |
$x^{18} + 12 x^{16} + 162 x^{15} + 60 x^{14} + 1620 x^{13} + 11182 x^{12} + 6480 x^{11} + 86328 x^{10} + 289170 x^{9} + 267852 x^{8} + 2515860 x^{7} + 17270941 x^{6} + 4503600 x^{5} + 35823300 x^{4} + 4796172 x^{3} + 35798328 x^{2} + 143350560 x + 436522680$ |
$29$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 27$ |
$x^{6} + 29$ |
$[0]$ |
$[2]$ |
| 29.18.15.2 |
$18$ |
$x^{18} + 1682 x^{6} - 658503$ |
$29$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 27$ |
$x^{6} + 29 t$ |
$[0]$ |
$[2]$ |
| 41.18.15.1 |
$18$ |
$x^{18} + 6 x^{16} + 210 x^{15} + 15 x^{14} + 1050 x^{13} + 18518 x^{12} + 2100 x^{11} + 72531 x^{10} + 644350 x^{9} + 112101 x^{8} + 2702700 x^{7} + 43833832 x^{6} + 2469390 x^{5} + 49507560 x^{4} + 55794550 x^{3} + 24820176 x^{2} + 271168590 x + 2029387125$ |
$41$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + t + 35$ |
$x^{6} + 41$ |
$[0]$ |
$[2]$ |
| 41.18.15.2 |
$18$ |
$x^{18} + 1681 x^{6} - 2412235$ |
$41$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + t + 35$ |
$x^{6} + 41 t$ |
$[0]$ |
$[2]$ |
| 47.18.15.1 |
$18$ |
$x^{18} + 6627 x^{6} - 4360566$ |
$47$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 42$ |
$x^{6} + 47 t$ |
$[0]$ |
$[2]$ |
| 47.18.15.2 |
$18$ |
$x^{18} + 18 x^{16} + 252 x^{15} + 135 x^{14} + 3780 x^{13} + 27141 x^{12} + 22680 x^{11} + 315351 x^{10} + 1253700 x^{9} + 1449333 x^{8} + 13970880 x^{7} + 84633402 x^{6} + 38789604 x^{5} + 304439355 x^{4} + 305802252 x^{3} + 454321656 x^{2} + 2092419000 x + 5952920804$ |
$47$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 42$ |
$x^{6} + 47$ |
$[0]$ |
$[2]$ |
| 53.18.15.1 |
$18$ |
$x^{18} + 18 x^{16} + 306 x^{15} + 135 x^{14} + 4590 x^{13} + 39714 x^{12} + 27540 x^{11} + 465579 x^{10} + 2330190 x^{9} + 2129733 x^{8} + 24730920 x^{7} + 164038368 x^{6} + 69954354 x^{5} + 649060200 x^{4} + 1093613706 x^{3} + 969968304 x^{2} + 5690051334 x + 18716241401$ |
$53$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 51$ |
$x^{6} + 53$ |
$[0]$ |
$[2]$ |
| 53.18.15.2 |
$18$ |
$x^{18} + 8427 x^{6} - 7592727$ |
$53$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 51$ |
$x^{6} + 53 t$ |
$[0]$ |
$[2]$ |
| 59.18.15.1 |
$18$ |
$x^{18} + 17405 x^{6} - 11706603$ |
$59$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 5 t + 57$ |
$x^{6} + 59 t$ |
$[0]$ |
$[2]$ |
| 59.18.15.2 |
$18$ |
$x^{18} + 30 x^{16} + 342 x^{15} + 375 x^{14} + 8550 x^{13} + 51412 x^{12} + 85500 x^{11} + 976995 x^{10} + 3626910 x^{9} + 7395375 x^{8} + 58140000 x^{7} + 263951626 x^{6} + 272804850 x^{5} + 1700151450 x^{4} + 2433470562 x^{3} + 4177869750 x^{2} + 16697221470 x + 36342813987$ |
$59$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 5 t + 57$ |
$x^{6} + 59$ |
$[0]$ |
$[2]$ |
| 71.18.15.1 |
$18$ |
$x^{18} + 20164 x^{6} - 22906304$ |
$71$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 64$ |
$x^{6} + 71 t$ |
$[0]$ |
$[2]$ |
| 71.18.15.2 |
$18$ |
$x^{18} + 24 x^{16} + 384 x^{15} + 240 x^{14} + 7680 x^{13} + 62933 x^{12} + 61440 x^{11} + 980064 x^{10} + 4807040 x^{9} + 5955504 x^{8} + 65041920 x^{7} + 390503059 x^{6} + 246816768 x^{5} + 2133356040 x^{4} + 3996794624 x^{3} + 4238775264 x^{2} + 23937335808 x + 72466644375$ |
$71$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 64$ |
$x^{6} + 71$ |
$[0]$ |
$[2]$ |
| 83.18.15.1 |
$18$ |
$x^{18} + 20667 x^{6} - 46314747$ |
$83$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 81$ |
$x^{6} + 83 t$ |
$[0]$ |
$[2]$ |
| 83.18.15.2 |
$18$ |
$x^{18} + 18 x^{16} + 486 x^{15} + 135 x^{14} + 7290 x^{13} + 99204 x^{12} + 43740 x^{11} + 1176219 x^{10} + 9751590 x^{9} + 5349483 x^{8} + 97671420 x^{7} + 886741518 x^{6} + 282739734 x^{5} + 4028689350 x^{4} + 14619279006 x^{3} + 6033836394 x^{2} + 59532739614 x + 293372245691$ |
$83$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 81$ |
$x^{6} + 83$ |
$[0]$ |
$[2]$ |
| 89.18.15.1 |
$18$ |
$x^{18} + 18 x^{16} + 516 x^{15} + 135 x^{14} + 7740 x^{13} + 111747 x^{12} + 46440 x^{11} + 1326087 x^{10} + 11712340 x^{9} + 6028263 x^{8} + 116765640 x^{7} + 1110998718 x^{6} + 338635836 x^{5} + 5109180705 x^{4} + 20112416316 x^{3} + 7653467412 x^{2} + 80535987936 x + 419455081800$ |
$89$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 86$ |
$x^{6} + 89$ |
$[0]$ |
$[2]$ |
| 89.18.15.2 |
$18$ |
$x^{18} + 23763 x^{6} - 60627334$ |
$89$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 86$ |
$x^{6} + 89 t$ |
$[0]$ |
$[2]$ |
| 101.18.15.1 |
$18$ |
$x^{18} + 18 x^{16} + 594 x^{15} + 135 x^{14} + 8910 x^{13} + 147858 x^{12} + 53460 x^{11} + 1758123 x^{10} + 18066510 x^{9} + 7981173 x^{8} + 177594120 x^{7} + 1875580176 x^{6} + 517626450 x^{5} + 8923750200 x^{4} + 42935829354 x^{3} + 13371857568 x^{2} + 164026444230 x + 971047065545$ |
$101$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 99$ |
$x^{6} + 101$ |
$[0]$ |
$[2]$ |
| 101.18.15.2 |
$18$ |
$x^{18} + 30603 x^{6} - 101999799$ |
$101$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 99$ |
$x^{6} + 101 t$ |
$[0]$ |
$[2]$ |
| 107.18.15.1 |
$18$ |
$x^{18} + 57245 x^{6} - 128629515$ |
$107$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 5 t + 105$ |
$x^{6} + 107 t$ |
$[0]$ |
$[2]$ |
| 107.18.15.2 |
$18$ |
$x^{18} + 30 x^{16} + 630 x^{15} + 375 x^{14} + 15750 x^{13} + 168196 x^{12} + 157500 x^{11} + 3304035 x^{10} + 22254750 x^{9} + 24945375 x^{8} + 354312000 x^{7} + 2405240122 x^{6} + 1718183250 x^{5} + 18866092650 x^{4} + 60921072450 x^{3} + 46919211750 x^{2} + 367798110750 x + 1380376857843$ |
$107$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 5 t + 105$ |
$x^{6} + 107$ |
$[0]$ |
$[2]$ |
| 113.18.15.1 |
$18$ |
$x^{18} + 48 x^{16} + 660 x^{15} + 960 x^{14} + 26400 x^{13} + 192079 x^{12} + 422400 x^{11} + 5847744 x^{10} + 28134700 x^{9} + 70218048 x^{8} + 661346400 x^{7} + 3147571759 x^{6} + 5075389440 x^{5} + 36870158160 x^{4} + 87592940600 x^{3} + 144538157184 x^{2} + 743524842720 x + 1825875840013$ |
$113$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 8 t + 110$ |
$x^{6} + 113$ |
$[0]$ |
$[2]$ |
| 113.18.15.2 |
$18$ |
$x^{18} + 102152 x^{6} - 158718670$ |
$113$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 8 t + 110$ |
$x^{6} + 113 t$ |
$[0]$ |
$[2]$ |
| 131.18.15.1 |
$18$ |
$x^{18} + 51483 x^{6} - 290003739$ |
$131$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 129$ |
$x^{6} + 131 t$ |
$[0]$ |
$[2]$ |
| 131.18.15.2 |
$18$ |
$x^{18} + 18 x^{16} + 774 x^{15} + 135 x^{14} + 11610 x^{13} + 250548 x^{12} + 69660 x^{11} + 2987163 x^{10} + 40607910 x^{9} + 13533723 x^{8} + 391280220 x^{7} + 5103045246 x^{6} + 1148449590 x^{5} + 25530484950 x^{4} + 173434221054 x^{3} + 38272301658 x^{2} + 622559906910 x + 4718315655755$ |
$131$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 129$ |
$x^{6} + 131$ |
$[0]$ |
$[2]$ |
| 137.18.15.1 |
$18$ |
$x^{18} + 36 x^{16} + 804 x^{15} + 540 x^{14} + 24120 x^{13} + 274071 x^{12} + 289440 x^{11} + 6463872 x^{10} + 47105020 x^{9} + 58446036 x^{8} + 881320680 x^{7} + 6110182575 x^{6} + 5155852608 x^{5} + 59711962860 x^{4} + 220204895544 x^{3} + 178117502472 x^{2} + 1507281043464 x + 5926050257733$ |
$137$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 6 t + 134$ |
$x^{6} + 137$ |
$[0]$ |
$[2]$ |
| 137.18.15.2 |
$18$ |
$x^{18} + 112614 x^{6} - 344561302$ |
$137$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 6 t + 134$ |
$x^{6} + 137 t$ |
$[0]$ |
$[2]$ |
| 149.18.15.1 |
$18$ |
$x^{18} + 18 x^{16} + 882 x^{15} + 135 x^{14} + 13230 x^{13} + 325122 x^{12} + 79380 x^{11} + 3880107 x^{10} + 60483150 x^{9} + 17565093 x^{8} + 578045160 x^{7} + 8401329984 x^{6} + 1701343602 x^{5} + 42919167240 x^{4} + 342747017802 x^{3} + 64348305552 x^{2} + 1201164636294 x + 10300987559321$ |
$149$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 147$ |
$x^{6} + 149$ |
$[0]$ |
$[2]$ |
| 149.18.15.2 |
$18$ |
$x^{18} + 66603 x^{6} - 486268503$ |
$149$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 3 t + 147$ |
$x^{6} + 149 t$ |
$[0]$ |
$[2]$ |
| 167.18.15.1 |
$18$ |
$x^{18} + 195223 x^{6} - 754509006$ |
$167$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 7 t + 162$ |
$x^{6} + 167 t$ |
$[0]$ |
$[2]$ |
| 167.18.15.2 |
$18$ |
$x^{18} + 42 x^{16} + 972 x^{15} + 735 x^{14} + 34020 x^{13} + 401021 x^{12} + 476280 x^{11} + 11030439 x^{10} + 84306420 x^{9} + 116205117 x^{8} + 1814354640 x^{7} + 12726449338 x^{6} + 12420382212 x^{5} + 148343449275 x^{4} + 592120006092 x^{3} + 515951235744 x^{2} + 4565618841672 x + 18431773475444$ |
$167$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 7 t + 162$ |
$x^{6} + 167$ |
$[0]$ |
$[2]$ |
| 173.18.15.1 |
$18$ |
$x^{18} + 12 x^{16} + 1026 x^{15} + 60 x^{14} + 10260 x^{13} + 439294 x^{12} + 41040 x^{11} + 3500856 x^{10} + 95648850 x^{9} + 10558092 x^{8} + 605432340 x^{7} + 14979518797 x^{6} + 1191563568 x^{5} + 52217993220 x^{4} + 748611549036 x^{3} + 52216354296 x^{2} + 1712702374560 x + 25448746759416$ |
$173$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 171$ |
$x^{6} + 173$ |
$[0]$ |
$[2]$ |
| 173.18.15.2 |
$18$ |
$x^{18} + 59858 x^{6} - 885389607$ |
$173$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 2 t + 171$ |
$x^{6} + 173 t$ |
$[0]$ |
$[2]$ |
| 179.18.15.1 |
$18$ |
$x^{18} + 128164 x^{6} - 1015155003$ |
$179$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 177$ |
$x^{6} + 179 t$ |
$[0]$ |
$[2]$ |
| 179.18.15.2 |
$18$ |
$x^{18} + 24 x^{16} + 1062 x^{15} + 240 x^{14} + 21240 x^{13} + 471752 x^{12} + 169920 x^{11} + 7505616 x^{10} + 106831890 x^{9} + 45248784 x^{8} + 1343621160 x^{7} + 17215341295 x^{6} + 5288012352 x^{5} + 119916735480 x^{4} + 900847464192 x^{3} + 239615658816 x^{2} + 4073420011968 x + 31281845110592$ |
$179$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 177$ |
$x^{6} + 179$ |
$[0]$ |
$[2]$ |
| 191.18.15.1 |
$18$ |
$x^{18} + 145924 x^{6} - 1198473812$ |
$191$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 172$ |
$x^{6} + 191 t$ |
$[0]$ |
$[2]$ |
| 191.18.15.2 |
$18$ |
$x^{18} + 24 x^{16} + 1032 x^{15} + 240 x^{14} + 20640 x^{13} + 445613 x^{12} + 165120 x^{11} + 7085664 x^{10} + 97501640 x^{9} + 42744624 x^{8} + 1234375200 x^{7} + 15632312083 x^{6} + 4848121344 x^{5} + 107169720840 x^{4} + 764262460112 x^{3} + 214138209504 x^{2} + 3518774284128 x + 26399210781039$ |
$191$ |
$6$ |
$3$ |
$15$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$6$ |
$[\ ]$ |
$[\ ]_{6}^{6}$ |
$t^{3} + 4 t + 172$ |
$x^{6} + 191$ |
$[0]$ |
$[2]$ |
