| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.18.1 |
$12$ |
$x^{12} - 8 x^{11} + 16 x^{10} + 64 x^{9} - 620 x^{8} - 7680 x^{7} + 12224 x^{6} + 203648 x^{5} + 795312 x^{4} + 1213568 x^{3} + 1855488 x^{2} + 2545152 x + 1772480$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 t^{2} x + 4 t^{5} + 12 t^{3} + 12 t^{2} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.10 |
$12$ |
$x^{12} + 24 x^{11} + 220 x^{10} + 80 x^{9} - 6036 x^{8} + 1216 x^{7} + 178592 x^{6} + 665728 x^{5} + 2382448 x^{4} - 2608256 x^{3} + 716736 x^{2} - 243456 x + 182080$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2} + 4\right) x + 8 t^{3} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.11 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} - 144 x^{9} + 8668 x^{8} - 36032 x^{7} + 196448 x^{6} - 771200 x^{5} + 1475568 x^{4} - 3364224 x^{3} + 5649728 x^{2} + 12790528 x + 10676800$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.12 |
$12$ |
$x^{12} - 20 x^{11} + 316 x^{10} - 3064 x^{9} + 21548 x^{8} - 105376 x^{7} + 379296 x^{6} - 877760 x^{5} + 1334896 x^{4} + 373696 x^{3} - 1816128 x^{2} + 8702592 x + 8239936$ |
$2$ |
$2$ |
$6$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.13 |
$12$ |
$x^{12} + 32 x^{11} + 532 x^{10} + 2944 x^{9} + 24252 x^{8} + 59520 x^{7} + 363872 x^{6} + 263936 x^{5} + 2174704 x^{4} - 449536 x^{3} + 8127808 x^{2} + 9509888 x + 9117760$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t + 4\right) x + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.14 |
$12$ |
$x^{12} - 12 x^{11} + 132 x^{10} - 1224 x^{9} + 9404 x^{8} - 20960 x^{7} + 226016 x^{6} + 258496 x^{5} + 3156720 x^{4} + 3669056 x^{3} + 31019072 x^{2} + 1809792 x + 1196096$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.15 |
$12$ |
$x^{12} - 12 x^{11} - 56 x^{9} + 2372 x^{8} + 8992 x^{7} + 115648 x^{6} + 164160 x^{5} + 1305648 x^{4} - 282560 x^{3} + 5591296 x^{2} - 9640320 x + 8497856$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 8 t^{5} + 4 t^{3} + 4 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.16 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 632 x^{9} + 3244 x^{8} + 12448 x^{7} + 29344 x^{6} + 151488 x^{5} + 499312 x^{4} + 678208 x^{3} + 3019712 x^{2} + 5071232 x + 4682560$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.17 |
$12$ |
$x^{12} + 12 x^{11} + 124 x^{10} + 328 x^{9} + 8076 x^{8} + 56800 x^{7} + 333472 x^{6} + 1195584 x^{5} + 3358576 x^{4} + 6370240 x^{3} + 9140672 x^{2} + 7707264 x + 4247872$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{4} + 8 t^{3} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.18 |
$12$ |
$x^{12} + 32 x^{11} + 356 x^{10} + 1376 x^{9} + 940 x^{8} + 18208 x^{6} + 37120 x^{5} + 219376 x^{4} + 87552 x^{3} + 2043200 x^{2} - 2284032 x + 610624$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4\right) x + 8 t^{5} + 4 t^{4} + 8 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.19 |
$12$ |
$x^{12} - 4 x^{11} + 12 x^{10} - 1464 x^{9} + 8348 x^{8} + 3680 x^{7} + 152224 x^{6} + 371008 x^{5} + 1270256 x^{4} + 2534080 x^{3} + 4709568 x^{2} + 4877952 x + 2395712$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3}\right) x + 4 t^{5} + 8 t^{4} + 8 t^{3} + 4 t^{2} + 4 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.2 |
$12$ |
$x^{12} + 32 x^{11} + 348 x^{10} + 736 x^{9} + 1772 x^{8} - 17664 x^{7} - 210784 x^{6} + 122624 x^{5} + 2220144 x^{4} - 783872 x^{3} + 273344 x^{2} - 563712 x + 182080$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4\right) x + 8 t^{3} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.20 |
$12$ |
$x^{12} + 8 x^{11} - 20 x^{10} - 1360 x^{9} + 7212 x^{8} + 79680 x^{7} + 403488 x^{6} + 1329536 x^{5} + 3255408 x^{4} + 6265472 x^{3} + 9350336 x^{2} + 9518848 x + 4682560$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.21 |
$12$ |
$x^{12} - 12 x^{11} + 76 x^{10} - 1064 x^{9} + 9132 x^{8} - 1248 x^{7} + 100384 x^{6} + 81088 x^{5} + 857712 x^{4} + 1515584 x^{3} + 3413696 x^{2} + 3749760 x + 4682560$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.22 |
$12$ |
$x^{12} - 12 x^{11} + 12 x^{10} - 776 x^{9} + 4492 x^{8} + 19168 x^{7} + 420576 x^{6} + 1449536 x^{5} + 5911280 x^{4} + 10930496 x^{3} + 23407552 x^{2} + 20938624 x + 6421312$ |
$2$ |
$2$ |
$6$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 12 t^{5} + 12 t^{4} + 8 t^{3} + 4 t^{2} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.23 |
$12$ |
$x^{12} - 12 x^{11} + 48 x^{10} - 344 x^{9} + 8244 x^{8} - 31136 x^{7} + 54848 x^{6} - 23104 x^{5} + 18864 x^{4} - 7360 x^{3} + 5120 x^{2} + 5760 x + 1472$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 4 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.24 |
$12$ |
$x^{12} + 8 x^{11} + 140 x^{10} - 1312 x^{9} + 9260 x^{8} - 11072 x^{7} - 34976 x^{6} + 349440 x^{5} - 387344 x^{4} + 175232 x^{3} + 3776960 x^{2} - 4825600 x + 12386624$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t\right) x + 8 t^{5} + 4 t^{4} + 12 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.25 |
$12$ |
$x^{12} - 20 x^{11} + 292 x^{10} - 2840 x^{9} + 18972 x^{8} - 90272 x^{7} + 343776 x^{6} - 825280 x^{5} + 1529840 x^{4} - 1040448 x^{3} + 101952 x^{2} + 1661056 x + 935488$ |
$2$ |
$2$ |
$6$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{2} + 8 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.26 |
$12$ |
$x^{12} + 24 x^{11} + 276 x^{10} + 1008 x^{9} - 7364 x^{8} - 73024 x^{7} - 69024 x^{6} + 1555840 x^{5} + 8919280 x^{4} + 23421824 x^{3} + 33939776 x^{2} + 26143488 x + 8417344$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2} + 4\right) x + 8 t^{5} + 8 t^{4} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.27 |
$12$ |
$x^{12} + 24 x^{11} + 300 x^{10} + 2480 x^{9} + 15084 x^{8} + 70848 x^{7} + 263968 x^{6} + 785280 x^{5} + 1858672 x^{4} + 3423104 x^{3} + 4742336 x^{2} + 4511488 x + 2639680$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 x + 8 t^{3} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.28 |
$12$ |
$x^{12} + 12 x^{11} + 128 x^{10} + 1032 x^{9} + 8068 x^{8} + 54752 x^{7} + 298816 x^{6} + 1148736 x^{5} + 2948656 x^{4} + 4481984 x^{3} + 2851584 x^{2} - 296320 x + 1412800$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 4 t^{5} + 12 t^{4} + 12 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.29 |
$12$ |
$x^{12} + 6 x^{11} + 18 x^{10} + 32 x^{9} + 38 x^{8} + 24 x^{7} + 16 x^{6} + 32 x^{5} + 44 x^{4} - 8 x^{3} + 8 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.3 |
$12$ |
$x^{12} + 4 x^{11} + 148 x^{10} + 600 x^{9} + 6524 x^{8} + 24224 x^{7} + 103520 x^{6} + 191168 x^{5} + 1586928 x^{4} + 6269248 x^{3} + 19370304 x^{2} + 18016128 x + 9253952$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{5} + 8 t^{4} + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.30 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{9} + 6 x^{8} + 32 x^{7} + 32 x^{6} + 28 x^{4} + 88 x^{3} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + 4 t + 2$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.31 |
$12$ |
$x^{12} - 4 x^{11} + 22 x^{10} + 16 x^{9} + 50 x^{8} + 32 x^{7} + 144 x^{6} + 96 x^{5} + 236 x^{4} + 248 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.32 |
$12$ |
$x^{12} + 6 x^{11} + 8 x^{10} - 8 x^{9} + 10 x^{8} + 64 x^{7} + 40 x^{6} + 48 x^{5} + 4 x^{4} + 56 x^{3} - 32 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.33 |
$12$ |
$x^{12} - 4 x^{11} + 4 x^{10} + 8 x^{9} + 18 x^{8} - 48 x^{7} + 24 x^{6} + 108 x^{4} - 144 x^{3} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^3:A_4$ (as 12T59) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 6$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.34 |
$12$ |
$x^{12} + 6 x^{11} + 18 x^{10} + 32 x^{9} + 50 x^{8} + 72 x^{7} + 112 x^{6} + 128 x^{5} + 140 x^{4} + 56 x^{3} + 168 x^{2} + 88$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 4 t^{2} + 6$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.35 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 12 x^{9} + 26 x^{8} + 48 x^{7} + 32 x^{6} - 8 x^{5} + 4 x^{4} - 8 x^{3} - 32 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.36 |
$12$ |
$x^{12} + 6 x^{11} + 16 x^{10} + 16 x^{9} - 6 x^{8} + 16 x^{7} + 64 x^{6} + 20 x^{4} + 72 x^{3} - 48 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:C_{12}$ (as 12T99) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{3} + 2 t x^{2} + 4 t^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.37 |
$12$ |
$x^{12} + 12 x^{9} + 2 x^{8} - 32 x^{7} - 16 x^{6} + 40 x^{5} + 52 x^{4} - 16 x^{2} + 8$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.38 |
$12$ |
$x^{12} - 4 x^{11} + 10 x^{10} - 8 x^{9} + 26 x^{8} - 8 x^{7} + 24 x^{6} + 16 x^{5} + 52 x^{4} + 32 x^{3} + 56 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.39 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{9} - 2 x^{8} - 8 x^{7} + 48 x^{6} - 4 x^{4} + 104 x^{3} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + 4 t^{2} + 2$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.4 |
$12$ |
$x^{12} + 8 x^{11} + 68 x^{10} - 2496 x^{9} + 13308 x^{8} - 24256 x^{7} + 30432 x^{6} - 58112 x^{5} + 57072 x^{4} - 42368 x^{3} + 204864 x^{2} + 227328 x + 160832$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t\right) x + 8 t^{4} + 4 t^{2} + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.40 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 16 x^{9} + 18 x^{8} + 40 x^{7} + 64 x^{6} + 64 x^{5} + 52 x^{4} + 88 x^{3} + 56 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.41 |
$12$ |
$x^{12} - 4 x^{11} + 4 x^{10} + 8 x^{9} + 10 x^{8} - 8 x^{7} + 56 x^{6} + 92 x^{4} + 128 x^{3} + 344$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:C_{12}$ (as 12T99) |
$12$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{12}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 4 t^{2} + 4 t + 6$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.42 |
$12$ |
$x^{12} + 6 x^{11} + 16 x^{10} + 16 x^{9} + 2 x^{8} + 24 x^{7} + 24 x^{6} - 48 x^{5} - 12 x^{4} - 8 x^{3} - 64 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:A_4$ (as 12T88) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{3} + 2 t x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.43 |
$12$ |
$x^{12} - 4 x^{11} + 26 x^{10} - 4 x^{9} + 22 x^{8} + 24 x^{7} + 80 x^{6} + 56 x^{5} + 44 x^{4} + 128 x^{3} + 8 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{3} + \left(2 t + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.44 |
$12$ |
$x^{12} - 4 x^{11} + 22 x^{10} - 4 x^{9} + 54 x^{8} + 64 x^{7} + 16 x^{6} + 56 x^{5} + 60 x^{4} - 32 x^{3} + 88 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.45 |
$12$ |
$x^{12} + 2 x^{11} + 22 x^{10} + 32 x^{9} + 50 x^{8} + 56 x^{7} + 80 x^{6} + 96 x^{5} + 52 x^{4} + 24 x^{3} + 56 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.46 |
$12$ |
$x^{12} + 2 x^{11} + 22 x^{10} + 52 x^{9} + 74 x^{8} + 56 x^{7} + 176 x^{6} + 168 x^{5} + 204 x^{4} + 72 x^{3} + 216 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.47 |
$12$ |
$x^{12} - 4 x^{11} + 16 x^{9} + 34 x^{8} + 32 x^{7} + 8 x^{6} - 16 x^{5} + 20 x^{4} + 32 x^{3} + 32 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:A_4$ (as 12T88) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 2 t^{2} x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.48 |
$12$ |
$x^{12} + 6 x^{11} + 18 x^{10} + 32 x^{9} + 34 x^{8} + 16 x^{7} - 8 x^{6} - 16 x^{5} - 12 x^{4} - 8 x^{3} - 8 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.49 |
$12$ |
$x^{12} + 2 x^{11} - 4 x^{10} + 12 x^{9} + 78 x^{8} + 96 x^{7} + 16 x^{6} + 72 x^{5} + 180 x^{4} + 248 x^{3} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4 \times C_2$ (as 12T7) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.5 |
$12$ |
$x^{12} - 4 x^{11} - 44 x^{10} - 344 x^{9} + 8636 x^{8} - 76064 x^{7} + 421728 x^{6} - 917440 x^{5} + 1522416 x^{4} + 1480896 x^{3} + 8253760 x^{2} - 2872192 x + 9117760$ |
$2$ |
$2$ |
$6$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t\right) x + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.50 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{9} + 34 x^{8} + 8 x^{7} + 72 x^{6} + 104 x^{5} + 52 x^{4} + 112 x^{3} + 128 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.51 |
$12$ |
$x^{12} + 2 x^{11} + 16 x^{10} + 44 x^{9} + 18 x^{8} - 8 x^{7} + 24 x^{6} + 40 x^{5} + 20 x^{4} + 8 x^{3} + 8$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4 \times C_2$ (as 12T7) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.52 |
$12$ |
$x^{12} + 10 x^{10} + 18 x^{8} - 8 x^{7} + 104 x^{6} + 48 x^{5} + 204 x^{4} + 216 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.53 |
$12$ |
$x^{12} + 2 x^{11} + 18 x^{10} + 56 x^{9} + 86 x^{8} + 88 x^{7} + 136 x^{6} + 192 x^{5} + 92 x^{4} + 120 x^{3} + 120 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^6:C_9$ (as 12T166) |
$9$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{9}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
| 2.12.18.54 |
$12$ |
$x^{12} + 2 x^{11} + 18 x^{10} + 36 x^{9} + 82 x^{8} + 64 x^{7} + 128 x^{6} + 72 x^{5} + 108 x^{4} + 72 x^{3} + 72 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^3:A_4$ (as 12T59) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[2]$ |
