| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.20.1 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 16 x^{9} + 24 x^{8} + 24 x^{7} + 18 x^{6} + 4 x^{5} - 8 x^{4} - 24 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.10 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 52 x^{8} - 12 x^{7} + 18 x^{6} + 40 x^{5} + 24 x^{4} + 32 x^{3} + 36 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + \left(4 t + 2\right) x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.11 |
$12$ |
$x^{12} + 2 x^{11} - 2 x^{10} + 12 x^{9} + 40 x^{8} + 4 x^{7} - 18 x^{6} + 12 x^{5} + 76 x^{4} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 6 t x^{4} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.12 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 16 x^{9} + 20 x^{8} + 16 x^{7} + 10 x^{6} - 12 x^{5} - 24 x^{3} + 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.13 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 12 x^{8} + 12 x^{7} + 26 x^{6} + 36 x^{5} + 48 x^{4} + 64 x^{3} + 52 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 2\right) x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.14 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 24 x^{9} + 40 x^{8} + 8 x^{7} + 18 x^{6} - 12 x^{5} - 32 x^{4} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 6 x^{4} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.15 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 28 x^{9} + 48 x^{8} + 32 x^{7} + 52 x^{6} + 32 x^{5} + 76 x^{4} + 24 x^{3} + 24 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2^3.S_4$ (as 12T107) |
$4$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 6 x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.16 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 8 x^{9} + 24 x^{8} + 16 x^{7} + 40 x^{6} + 52 x^{4} + 24 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 4\right) x^{4} + \left(4 t + 6\right) x^{2} + 4 t + 2$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.17 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} - 4 x^{9} + 16 x^{8} - 12 x^{7} + 26 x^{6} + 16 x^{5} + 40 x^{4} + 12 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{4} + 6 x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.18 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 12 x^{9} + 24 x^{8} + 12 x^{7} + 26 x^{6} + 4 x^{5} + 80 x^{4} + 24 x^{3} + 20 x^{2} + 32 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 t x^{3} + 2 x^{2} + 4 t x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.19 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 12 x^{9} + 28 x^{8} + 36 x^{7} + 74 x^{6} + 48 x^{5} + 72 x^{4} + 8 x^{3} + 44 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.2 |
$12$ |
$x^{12} + 4 x^{11} + 10 x^{10} + 8 x^{9} + 30 x^{8} + 24 x^{7} + 76 x^{6} + 72 x^{5} + 120 x^{4} + 40 x^{3} + 60 x^{2} + 8 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(6 t + 6\right) x^{4} + 4 t x^{3} + \left(6 t + 4\right) x^{2} + 4 t x + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.20 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 24 x^{9} + 48 x^{8} + 40 x^{7} + 36 x^{6} + 24 x^{5} + 20 x^{4} + 16 x^{3} + 8 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.21 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 16 x^{9} + 8 x^{8} - 20 x^{7} + 12 x^{6} + 52 x^{5} + 40 x^{4} + 32 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + 4 x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.22 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 4 x^{9} + 22 x^{8} + 20 x^{7} + 34 x^{6} + 8 x^{5} + 72 x^{4} + 48 x^{3} + 16 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + 6 t x^{2} + 4 t x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.23 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 32 x^{8} + 8 x^{7} + 10 x^{6} - 12 x^{5} + 16 x^{4} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.24 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 64 x^{8} - 36 x^{7} + 90 x^{6} - 8 x^{5} + 48 x^{4} + 32 x^{3} + 12 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + 6 x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.25 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 28 x^{8} - 4 x^{7} + 24 x^{6} + 24 x^{5} + 68 x^{4} + 24 x^{3} + 40 x^{2} + 8 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 2\right) x^{2} + 4 t x + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.26 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 4 x^{9} + 18 x^{6} - 20 x^{5} - 8 x^{4} + 48 x^{3} - 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 t x^{3} + 2 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.27 |
$12$ |
$x^{12} - 2 x^{11} - 2 x^{10} + 28 x^{9} + 56 x^{8} + 12 x^{7} - 12 x^{6} + 28 x^{5} + 48 x^{4} + 40 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.28 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 20 x^{9} + 44 x^{8} + 56 x^{7} + 66 x^{6} + 28 x^{5} + 40 x^{4} + 24 x^{3} + 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 6\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.29 |
$12$ |
$x^{12} - 2 x^{11} + 10 x^{10} + 8 x^{9} + 4 x^{8} + 36 x^{7} + 36 x^{6} + 4 x^{5} + 48 x^{4} + 32 x^{3} + 24 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.3 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 16 x^{9} - 4 x^{8} + 4 x^{7} + 36 x^{6} + 4 x^{5} + 16 x^{4} + 32 x^{3} + 24 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.30 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 16 x^{9} + 28 x^{8} + 32 x^{7} + 26 x^{6} + 20 x^{5} + 16 x^{4} - 24 x^{3} + 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.31 |
$12$ |
$x^{12} - 2 x^{11} + 10 x^{10} - 4 x^{9} + 32 x^{8} - 4 x^{7} + 36 x^{6} - 4 x^{5} + 40 x^{4} + 8 x^{3} + 16 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\wr S_3$ (as 12T135) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 4\right) x^{4} + 4 t x^{3} + 2 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.32 |
$12$ |
$x^{12} + 2 x^{11} + 10 x^{10} + 20 x^{9} + 32 x^{8} + 36 x^{7} + 46 x^{6} + 60 x^{5} + 36 x^{4} - 24 x^{3} - 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 4\right) x^{4} + 4 x^{3} + 6 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.33 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 20 x^{9} + 38 x^{8} + 12 x^{7} + 48 x^{6} + 44 x^{5} + 40 x^{4} - 8 x^{3} + 76 x^{2} - 24 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2^3:S_4$ (as 12T106) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(6 t + 4\right) x^{4} + \left(2 t + 6\right) x^{2} + 4 t x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.34 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 24 x^{9} + 44 x^{8} + 32 x^{7} + 48 x^{6} + 16 x^{5} + 68 x^{4} + 32 x^{3} + 24 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$S_4$ (as 12T9) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 4 x^{3} + \left(4 t + 2\right) x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.35 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 40 x^{8} + 32 x^{7} + 44 x^{6} + 72 x^{5} + 68 x^{4} + 96 x^{3} + 88 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.36 |
$12$ |
$x^{12} + 2 x^{11} + 10 x^{10} + 8 x^{9} + 32 x^{8} + 12 x^{7} + 46 x^{6} - 12 x^{5} + 36 x^{4} + 48 x^{3} - 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t + 4\right) x^{4} + 4 t x^{3} + 6 x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.37 |
$12$ |
$x^{12} + 10 x^{11} + 51 x^{10} + 176 x^{9} + 450 x^{8} + 870 x^{7} + 1299 x^{6} + 1516 x^{5} + 1250 x^{4} + 542 x^{3} + 67 x^{2} - 56 x + 7$ |
$2$ |
$6$ |
$2$ |
$20$ |
$S_4$ (as 12T9) |
$2$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.38 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 4 x^{9} + 8 x^{8} + 24 x^{7} + 68 x^{6} + 16 x^{5} + 44 x^{4} + 24 x^{3} + 88 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2^3.S_4$ (as 12T107) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 4 t x^{3} + 6 x^{2} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.39 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 20 x^{9} + 40 x^{8} + 48 x^{7} + 44 x^{6} + 32 x^{5} + 52 x^{4} + 24 x^{3} + 24 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2^2:S_4$ (as 12T69) |
$2$ |
$3$ |
$[8/3]$ |
$[4/3, 4/3, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 2 x^{2} + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.4 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{10} + 16 x^{9} + 20 x^{8} + 8 x^{7} + 26 x^{6} + 52 x^{5} + 44 x^{4} + 8 x^{3} + 20 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(4 t + 4\right) x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.40 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 24 x^{8} + 32 x^{7} + 28 x^{6} + 24 x^{5} + 36 x^{4} + 48 x^{3} + 88 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + 6 x^{2} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.41 |
$12$ |
$x^{12} - 2 x^{11} + 2 x^{10} + 12 x^{9} + 24 x^{8} - 4 x^{7} + 12 x^{6} + 28 x^{5} + 40 x^{4} + 40 x^{3} + 48 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + 4 t + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.42 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 12 x^{8} + 8 x^{7} + 46 x^{6} + 12 x^{5} + 24 x^{4} + 28 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + \left(4 t + 2\right) x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.43 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} + 8 x^{9} + 20 x^{8} + 4 x^{7} + 42 x^{6} + 40 x^{5} + 40 x^{4} + 16 x^{3} + 40 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x^{4} + \left(4 t + 4\right) x^{2} + 4 t x + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.44 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 16 x^{9} + 52 x^{8} - 24 x^{7} + 18 x^{6} + 16 x^{5} + 12 x^{4} + 32 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{3} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.45 |
$12$ |
$x^{12} + 4 x^{11} + 16 x^{10} + 24 x^{9} + 36 x^{8} + 4 x^{7} + 10 x^{6} + 28 x^{5} + 24 x^{4} + 24 x^{3} + 52 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 6 x^{4} + \left(4 t + 2\right) x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.46 |
$12$ |
$x^{12} + 2 x^{11} + 6 x^{10} + 16 x^{9} + 44 x^{8} + 52 x^{7} + 54 x^{6} + 20 x^{5} + 76 x^{4} + 48 x^{3} + 12 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(6 t + 4\right) x^{4} + 4 t x^{3} + \left(4 t + 6\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.47 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 20 x^{8} + 24 x^{7} + 46 x^{6} + 12 x^{5} + 40 x^{4} + 32 x^{3} + 52 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 2\right) x^{4} + \left(4 t + 6\right) x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.48 |
$12$ |
$x^{12} - 2 x^{11} + 12 x^{10} + 8 x^{9} + 36 x^{8} + 40 x^{7} + 18 x^{6} + 16 x^{5} + 44 x^{4} + 40 x^{3} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 6\right) x^{4} + \left(4 t + 4\right) x^{3} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.49 |
$12$ |
$x^{12} + 4 x^{11} + 12 x^{10} + 16 x^{9} + 32 x^{8} + 16 x^{7} + 38 x^{6} + 44 x^{5} + 40 x^{4} + 16 x^{3} + 28 x^{2} + 24 x + 12$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t + 6\right) x^{4} + 2 x^{2} + 4 x + 2 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.5 |
$12$ |
$x^{12} - 2 x^{11} + 16 x^{10} - 12 x^{9} + 32 x^{8} + 16 x^{7} - 22 x^{6} + 16 x^{5} + 28 x^{4} + 32 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 6 x^{4} + 4 t x^{2} + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.50 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 24 x^{8} + 36 x^{7} + 50 x^{6} + 36 x^{5} + 72 x^{4} + 64 x^{3} + 28 x^{2} + 40 x + 28$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[8/3]$ |
$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 6 x^{2} + \left(4 t + 4\right) x + 6 t + 4$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.51 |
$12$ |
$x^{12} + 2 x^{11} - 2 x^{10} + 16 x^{9} + 52 x^{8} + 36 x^{7} + 46 x^{6} + 36 x^{5} + 84 x^{4} + 24 x^{3} + 36 x^{2} + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[8/3]$ |
$[2, 2, 8/3, 8/3, 8/3, 8/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 6 t x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 2\right) x^{2} + 6 t$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.52 |
$12$ |
$x^{12} - 2 x^{11} + 6 x^{10} + 24 x^{9} + 20 x^{8} + 16 x^{7} + 20 x^{6} - 4 x^{5} + 44 x^{4} + 48 x^{3} + 16 x^{2} + 48 x + 36$ |
$2$ |
$6$ |
$2$ |
$20$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[8/3]$ |
$[2, 8/3, 8/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(6 t + 4\right) x^{4} + 4 x^{3} + 4 x + 6$ |
$[5, 0]$ |
$[1, 1]$ |
| 2.12.20.53 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2$ |
$2$ |
$12$ |
$1$ |
$20$ |
$S_3\times A_4$ (as 12T43) |
$6$ |
$3$ |
$[2, 2]$ |
$[2, 2]_{3}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{8} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[3, 2]$ |
| 2.12.20.54 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{6} + 2$ |
$2$ |
$12$ |
$1$ |
$20$ |
$C_2^4:(S_3\times A_4)$ (as 12T206) |
$6$ |
$3$ |
$[2, 2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[3, 2]$ |
