| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.31 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 6 x^{8} + 12 x^{7} + 32 x^{6} + 48 x^{5} + 76 x^{4} + 48 x^{3} + 40 x^{2} + 8 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.12.32 |
$12$ |
$x^{12} - 4 x^{10} - 4 x^{9} + 26 x^{8} + 40 x^{7} - 4 x^{6} - 40 x^{5} + 28 x^{4} + 72 x^{3} + 24 x^{2} - 16 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$A_4\wr C_2$ (as 12T129) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{2} + \left(2 t^{2} + 2 t\right) x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.12.33 |
$12$ |
$x^{12} + 2 x^{10} + 6 x^{9} + 6 x^{8} + 8 x^{7} + 28 x^{6} + 24 x^{5} + 20 x^{4} + 24 x^{3} + 32 x^{2} + 24 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + 2 x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 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) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + \left(2 t + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.30 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{9} + 6 x^{8} + 32 x^{7} + 32 x^{6} + 28 x^{4} + 88 x^{3} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (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) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + 4 t^{2} + 2$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.40 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 16 x^{9} + 18 x^{8} + 40 x^{7} + 64 x^{6} + 64 x^{5} + 52 x^{4} + 88 x^{3} + 56 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (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) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.50 |
$12$ |
$x^{12} - 4 x^{11} + 28 x^{9} + 34 x^{8} + 8 x^{7} + 72 x^{6} + 104 x^{5} + 52 x^{4} + 112 x^{3} + 128 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (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) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.55 |
$12$ |
$x^{12} + 4 x^{9} + 22 x^{8} + 8 x^{7} - 40 x^{6} + 72 x^{5} + 132 x^{4} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2\wr C_6$ (as 12T142) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + 2 t^{2} x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.56 |
$12$ |
$x^{12} + 2 x^{11} + 18 x^{10} + 36 x^{9} + 62 x^{8} + 56 x^{7} + 96 x^{6} + 136 x^{5} + 44 x^{4} + 120 x^{3} + 104 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:C_{12}$ (as 12T99) |
$12$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{12}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 2\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.57 |
$12$ |
$x^{12} + 2 x^{11} - 4 x^{10} + 12 x^{9} + 70 x^{8} + 56 x^{7} + 32 x^{6} + 168 x^{5} + 164 x^{4} + 104 x^{3} + 160 x^{2} + 88$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 t^{2} + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.58 |
$12$ |
$x^{12} - 4 x^{11} + 16 x^{9} + 26 x^{8} + 48 x^{7} + 72 x^{6} + 80 x^{5} + 100 x^{4} + 96 x^{3} + 96 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^4:C_{12}$ (as 12T99) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + 2 t^{2} x^{2} + 4 t^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.59 |
$12$ |
$x^{12} + 6 x^{11} + 22 x^{10} + 56 x^{9} + 126 x^{8} + 240 x^{7} + 332 x^{6} - 18 x^{5} - 459 x^{4} - 394 x^{3} - 344 x^{2} + 138 x + 423$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4$ (as 12T4) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.60 |
$12$ |
$x^{12} + 10 x^{10} + 6 x^{8} + 8 x^{7} + 8 x^{6} - 48 x^{5} + 44 x^{4} - 64 x^{3} - 8 x^{2} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^2 \times A_4$ (as 12T26) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 2$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.61 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 4 x^{9} + 10 x^{8} + 16 x^{7} + 56 x^{6} - 8 x^{5} + 52 x^{4} + 8 x^{3} + 112 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 2\right) x^{3} + 2 t^{2} x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.62 |
$12$ |
$x^{12} + 10 x^{10} + 18 x^{8} + 8 x^{7} + 72 x^{6} - 16 x^{5} + 204 x^{4} + 248 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$C_2^2 \times A_4$ (as 12T26) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.63 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 8 x^{9} + 6 x^{8} + 24 x^{7} + 24 x^{6} + 28 x^{4} + 56 x^{3} - 24$ |
$2$ |
$4$ |
$3$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 4 t + 2$ |
$[3, 3, 0]$ |
$[2]$ |
| 2.12.18.64 |
$12$ |
$x^{12} - 4 x^{11} + 6 x^{10} + 12 x^{9} + 58 x^{8} + 8 x^{7} + 96 x^{6} + 40 x^{5} + 236 x^{4} + 248 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t^{2} x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[2]$ |
| 2.12.18.65 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 8 x^{9} + 10 x^{8} + 40 x^{7} + 40 x^{6} + 92 x^{4} + 184 x^{3} + 344$ |
$2$ |
$4$ |
$3$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 4 t^{2} + 4 t + 6$ |
$[3, 3, 0]$ |
$[2]$ |
| 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) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + 4 t x + 4 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
