Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.12.24.1 |
$12$ |
$x^{12} + 12 x^{10} + 62 x^{8} + 32 x^{7} + 144 x^{6} + 16 x^{5} + 60 x^{4} - 64 x^{3} - 16 x^{2} - 96 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 4 t x + 4 t^{2} + 4 t + 2$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.10 |
$12$ |
$x^{12} + 12 x^{11} + 64 x^{10} + 76 x^{9} + 146 x^{8} + 336 x^{7} + 448 x^{6} + 336 x^{5} + 876 x^{4} + 496 x^{3} + 384 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.100 |
$12$ |
$x^{12} + 14 x^{10} + 4 x^{9} + 98 x^{8} + 56 x^{7} + 432 x^{6} + 432 x^{5} + 1164 x^{4} + 1168 x^{3} + 1240 x^{2} + 976 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T88) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.101 |
$12$ |
$x^{12} + 12 x^{11} + 70 x^{10} + 192 x^{9} + 478 x^{8} + 824 x^{7} + 1344 x^{6} + 2976 x^{5} + 4156 x^{4} + 4480 x^{3} + 7096 x^{2} + 2176 x + 4072$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T88) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t^{2} + 2 t + 6\right) x^{2} + 4 t^{2} x + 12 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.102 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 40 x^{9} - 30 x^{8} + 328 x^{7} + 1008 x^{6} + 736 x^{5} + 988 x^{4} + 3232 x^{3} + 1752 x^{2} + 448 x + 3032$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T88) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 2 t + 2\right) x^{2} + 4 t^{2} x + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.103 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 180 x^{9} + 338 x^{8} + 496 x^{7} + 720 x^{6} + 1024 x^{5} + 1260 x^{4} + 1328 x^{3} + 1368 x^{2} + 1104 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.104 |
$12$ |
$x^{12} - 12 x^{10} - 8 x^{9} + 186 x^{8} + 120 x^{7} + 280 x^{6} + 224 x^{5} + 1236 x^{4} + 1840 x^{3} + 3952 x^{2} + 2176 x + 4072$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t\right) x^{2} + 4 t^{2} x + 12 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.105 |
$12$ |
$x^{12} + 8 x^{10} - 8 x^{9} + 42 x^{8} + 16 x^{7} + 320 x^{6} + 384 x^{5} + 1236 x^{4} + 1376 x^{3} + 3152 x^{2} + 2816 x + 3624$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.106 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 200 x^{9} + 390 x^{8} + 600 x^{7} + 920 x^{6} + 1904 x^{5} + 1484 x^{4} + 1664 x^{3} + 2552 x^{2} + 416 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 6\right) x^{2} + 4 t^{2} x + 4 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.107 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 64 x^{9} + 86 x^{8} + 488 x^{7} + 1000 x^{6} + 320 x^{5} + 1044 x^{4} + 672 x^{3} + 576 x^{2} + 224 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^2 \times A_4$ (as 12T25) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + 4 t x + 4 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.108 |
$12$ |
$x^{12} + 12 x^{11} + 40 x^{10} + 4 x^{9} + 30 x^{8} + 712 x^{7} + 600 x^{6} + 1248 x^{5} + 1332 x^{4} + 2016 x^{3} + 2336 x^{2} + 1584 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T89) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6 t\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.109 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 188 x^{9} + 418 x^{8} + 768 x^{7} + 1312 x^{6} + 2032 x^{5} + 2988 x^{4} + 3984 x^{3} + 5816 x^{2} + 2544 x + 6392$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + 4 x + 12 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.11 |
$12$ |
$x^{12} - 8 x^{11} + 90 x^{10} - 28 x^{9} + 450 x^{8} + 624 x^{7} + 1760 x^{6} + 768 x^{5} + 636 x^{4} - 384 x^{3} + 2632 x^{2} + 2352 x + 2744$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 2 t + 6\right) x^{2} + 4 x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.110 |
$12$ |
$x^{12} - 8 x^{11} + 28 x^{10} + 64 x^{9} + 166 x^{8} + 296 x^{7} + 912 x^{6} + 704 x^{5} + 2212 x^{4} + 784 x^{3} + 3424 x^{2} + 928 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^2 \times A_4$ (as 12T26) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.111 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 52 x^{9} + 86 x^{8} + 544 x^{7} + 896 x^{6} + 1744 x^{5} + 2660 x^{4} + 4944 x^{3} + 4088 x^{2} + 3888 x + 4568$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.112 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 148 x^{9} + 210 x^{8} + 160 x^{7} + 256 x^{6} + 928 x^{5} + 2436 x^{4} + 3440 x^{3} + 2920 x^{2} + 912 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.113 |
$12$ |
$x^{12} - 8 x^{11} + 84 x^{10} - 36 x^{9} + 418 x^{8} + 368 x^{7} + 912 x^{6} + 368 x^{5} + 524 x^{4} + 256 x^{3} + 528 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4\right) x^{2} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.114 |
$12$ |
$x^{12} + 14 x^{10} + 12 x^{9} + 22 x^{8} - 32 x^{7} + 272 x^{6} + 832 x^{5} + 796 x^{4} + 800 x^{3} + 952 x^{2} + 1392 x + 1096$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.115 |
$12$ |
$x^{12} + 10 x^{10} + 36 x^{9} + 38 x^{8} - 8 x^{7} + 264 x^{6} + 912 x^{5} + 540 x^{4} + 368 x^{3} + 1912 x^{2} + 1008 x + 712$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T89) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.116 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 76 x^{9} + 198 x^{8} + 656 x^{7} + 984 x^{6} + 960 x^{5} + 2644 x^{4} + 3632 x^{3} + 2112 x^{2} + 2544 x + 4568$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.(C_2\times A_4)$ (as 12T143) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 2 t\right) x^{2} + 4 x + 8 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.117 |
$12$ |
$x^{12} + 12 x^{10} + 8 x^{9} - 198 x^{8} - 328 x^{7} - 872 x^{6} - 2176 x^{5} - 2076 x^{4} - 3664 x^{3} - 2768 x^{2} - 1824 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 6 t\right) x^{2} + 4 t x + 12 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.118 |
$12$ |
$x^{12} + 18 x^{10} - 8 x^{9} + 146 x^{8} + 24 x^{7} + 464 x^{6} + 64 x^{5} + 1228 x^{4} + 656 x^{3} + 968 x^{2} + 1184 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3:A_4$ (as 12T59) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.119 |
$12$ |
$x^{12} - 8 x^{11} + 84 x^{10} - 48 x^{9} + 462 x^{8} + 160 x^{7} + 480 x^{6} + 592 x^{5} + 284 x^{4} + 352 x^{3} + 240 x^{2} + 32 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[4/3, 4/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4\right) x^{2} + 4 t x + 4 t^{2} + 2$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.12 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 52 x^{9} + 94 x^{8} + 552 x^{7} + 912 x^{6} + 2528 x^{5} + 1724 x^{4} + 2816 x^{3} - 296 x^{2} + 560 x - 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T88) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6 t + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.120 |
$12$ |
$x^{12} + 18 x^{10} + 20 x^{9} - 130 x^{8} - 200 x^{7} - 352 x^{6} - 544 x^{5} + 156 x^{4} + 176 x^{3} + 1256 x^{2} + 1424 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 6 t + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.121 |
$12$ |
$x^{12} + 4 x^{11} + 70 x^{10} + 212 x^{9} + 206 x^{8} + 752 x^{7} + 688 x^{6} + 896 x^{5} + 1300 x^{4} + 944 x^{3} + 600 x^{2} + 976 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t^{2} + 4\right) x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.122 |
$12$ |
$x^{12} - 8 x^{11} + 16 x^{10} + 100 x^{9} + 314 x^{8} + 848 x^{7} + 1784 x^{6} + 2704 x^{5} + 3588 x^{4} + 4128 x^{3} + 3360 x^{2} + 2128 x + 1928$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.123 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 50 x^{8} + 136 x^{7} + 224 x^{6} + 288 x^{5} + 140 x^{4} + 592 x^{3} + 664 x^{2} + 1776 x + 632$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4 \times C_2$ (as 12T7) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.124 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 114 x^{8} + 72 x^{7} + 480 x^{6} + 752 x^{5} + 2340 x^{4} + 2672 x^{3} + 4672 x^{2} + 2480 x + 2728$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.125 |
$12$ |
$x^{12} - 8 x^{11} + 80 x^{10} - 32 x^{9} + 30 x^{8} + 104 x^{7} + 80 x^{6} - 272 x^{5} + 436 x^{4} + 1328 x^{3} + 112 x^{2} + 1728 x + 2392$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^2 \times A_4$ (as 12T25) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 2 t x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.126 |
$12$ |
$x^{12} + 16 x^{10} + 68 x^{9} - 94 x^{8} + 16 x^{7} + 992 x^{6} + 752 x^{5} + 948 x^{4} + 320 x^{3} + 336 x^{2} - 16 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.(C_2\times A_4)$ (as 12T143) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 6 t + 4\right) x^{2} + 4 x + 4 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.127 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 144 x^{9} + 242 x^{8} + 368 x^{7} + 688 x^{6} + 1120 x^{5} + 1956 x^{4} + 1104 x^{3} + 1096 x^{2} - 704 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + 4 t x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.128 |
$12$ |
$x^{12} + 26 x^{10} - 12 x^{9} + 182 x^{8} + 384 x^{7} + 448 x^{6} + 1040 x^{5} + 1252 x^{4} + 1056 x^{3} + 1128 x^{2} + 624 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.129 |
$12$ |
$x^{12} + 16 x^{10} - 56 x^{9} + 14 x^{8} - 40 x^{7} - 200 x^{6} - 368 x^{5} + 388 x^{4} + 1200 x^{3} + 1344 x^{2} + 2144 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 t x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.13 |
$12$ |
$x^{12} - 8 x^{11} + 94 x^{10} - 48 x^{9} + 514 x^{8} + 264 x^{7} + 1400 x^{6} + 1856 x^{5} + 2204 x^{4} + 3760 x^{3} + 2408 x^{2} + 2208 x + 2264$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(2 t^{2} + 4 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.130 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 116 x^{9} + 162 x^{8} + 200 x^{7} + 640 x^{6} + 1792 x^{5} + 3964 x^{4} + 5536 x^{3} + 6360 x^{2} + 3888 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.131 |
$12$ |
$x^{12} + 8 x^{10} - 4 x^{9} + 66 x^{8} - 208 x^{7} + 320 x^{6} + 368 x^{5} + 460 x^{4} - 32 x^{3} + 96 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t^{2} x^{2} + \left(4 t + 4\right) x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.132 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 132 x^{9} + 262 x^{8} + 760 x^{7} + 1544 x^{6} + 1632 x^{5} + 2324 x^{4} + 4224 x^{3} + 2464 x^{2} + 784 x + 2744$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.(C_2\times A_4)$ (as 12T143) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.133 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 148 x^{9} + 262 x^{8} + 552 x^{7} + 1144 x^{6} + 1408 x^{5} + 1532 x^{4} + 3232 x^{3} + 1576 x^{2} + 2960 x + 968$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T89) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 6 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.134 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 56 x^{9} + 10 x^{8} + 192 x^{7} + 520 x^{6} + 688 x^{5} + 932 x^{4} + 688 x^{3} + 576 x^{2} + 224 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + 4 t^{2} x + 4 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.135 |
$12$ |
$x^{12} - 8 x^{11} + 78 x^{10} + 76 x^{9} - 30 x^{8} + 480 x^{7} + 1728 x^{6} + 2304 x^{5} + 1428 x^{4} + 3232 x^{3} + 2776 x^{2} - 144 x + 1768$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^2 \times A_4$ (as 12T25) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + 4 x + 12 t^{2} + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.136 |
$12$ |
$x^{12} + 22 x^{10} + 60 x^{9} + 46 x^{8} + 336 x^{7} + 1160 x^{6} + 2560 x^{5} + 4428 x^{4} + 4672 x^{3} + 4648 x^{2} + 2288 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T89) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.137 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 136 x^{9} + 186 x^{8} + 328 x^{7} + 920 x^{6} + 1312 x^{5} + 1356 x^{4} + 1952 x^{3} + 3064 x^{2} - 384 x + 2232$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 2 t + 6\right) x^{2} + 4 t^{2} x + 4 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.138 |
$12$ |
$x^{12} - 8 x^{11} + 24 x^{10} + 68 x^{9} + 178 x^{8} + 408 x^{7} + 1376 x^{6} + 1536 x^{5} + 2900 x^{4} + 4432 x^{3} + 3952 x^{2} + 3472 x + 2728$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.(C_2\times A_4)$ (as 12T143) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.139 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 82 x^{8} + 48 x^{7} + 216 x^{6} + 464 x^{5} + 748 x^{4} + 1280 x^{3} + 2728 x^{2} + 2160 x + 3064$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 2\right) x^{2} + 4 x + 4 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.14 |
$12$ |
$x^{12} + 18 x^{10} - 16 x^{9} - 58 x^{8} + 96 x^{7} + 48 x^{6} + 956 x^{4} + 1280 x^{3} + 2120 x^{2} + 1056 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 4 t + 2\right) x^{2} + 4 t^{2} x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.140 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 216 x^{9} + 454 x^{8} + 744 x^{7} + 1128 x^{6} + 1616 x^{5} + 1388 x^{4} + 2304 x^{3} + 2872 x^{2} + 2080 x + 3624$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 6\right) x^{2} + 4 t^{2} x + 12 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.141 |
$12$ |
$x^{12} - 6 x^{10} + 4 x^{9} + 2 x^{8} + 40 x^{7} + 488 x^{6} + 816 x^{5} + 1916 x^{4} + 2416 x^{3} + 3352 x^{2} + 1776 x + 632$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4\wr C_3$ (as 12T94) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 2\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
2.12.24.142 |
$12$ |
$x^{12} + 16 x^{10} - 52 x^{9} + 18 x^{8} + 64 x^{7} + 144 x^{6} + 144 x^{5} + 108 x^{4} + 64 x^{3} + 288 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[8/3, 8/3]$ |
$[8/3, 8/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 x + 6$ |
$[5, 4, 0]$ |
$[1]$ |
2.12.24.143 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 128 x^{9} + 202 x^{8} + 408 x^{7} + 896 x^{6} + 1584 x^{5} + 1988 x^{4} + 1888 x^{3} + 2064 x^{2} - 64 x + 2376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^2 \times A_4$ (as 12T26) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + 4 t x + 8 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |