| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.23.1 |
$12$ |
$x^{12} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.10 |
$12$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 9 x^{4} + 6 x^{3} + 9 x^{2} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 9 x^{4} + 6 x^{3} + 9 x^{2} + 9 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.100 |
$12$ |
$x^{12} + 6 x^{9} + 12 x^{6} + 9 x^{4} + 9 x^{3} + 9 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 12 x^{6} + 9 x^{4} + 9 x^{3} + 9 x^{2} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.101 |
$12$ |
$x^{12} + 6 x^{6} + 9 x^{5} + 9 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 9 x^{5} + 9 x^{3} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.102 |
$12$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{4} + 3 x^{3} + 18 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{4} + 3 x^{3} + 18 x^{2} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.103 |
$12$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 18 x^{4} + 18 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 18 x^{4} + 18 x^{3} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.104 |
$12$ |
$x^{12} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 9 x^{2} + 18 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 9 x^{2} + 18 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.105 |
$12$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 18 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 18 x^{5} + 18 x^{3} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.106 |
$12$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 9 x^{5} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 9 x^{5} + 9 x + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.107 |
$12$ |
$x^{12} + 9 x^{6} + 18 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 9 x^{6} + 18 x^{4} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.108 |
$12$ |
$x^{12} + 24 x^{6} + 9 x^{2} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 9 x^{2} + 9 x + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.109 |
$12$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3:D_{12}$ (as 12T38) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 15 x^{6} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.11 |
$12$ |
$x^{12} + 3 x^{9} + 18 x^{5} + 9 x^{3} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 18 x^{5} + 9 x^{3} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.110 |
$12$ |
$x^{12} + 24 x^{6} + 9 x^{4} + 18 x^{3} + 9 x^{2} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 9 x^{4} + 18 x^{3} + 9 x^{2} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.111 |
$12$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 18 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 18 x^{3} + 9 x^{2} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.112 |
$12$ |
$x^{12} + 21 x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.113 |
$12$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 18 x^{4} + 18 x^{3} + 18 x^{2} + 18 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 18 x^{4} + 18 x^{3} + 18 x^{2} + 18 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.114 |
$12$ |
$x^{12} + 6 x^{6} + 18 x^{3} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 18 x^{3} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.115 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{3} + 9 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{3} + 9 x^{2} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.116 |
$12$ |
$x^{12} + 3 x^{9} + 12 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 12 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.117 |
$12$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 18 x^{4} + 21 x^{3} + 18 x^{2} + 18 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 9 x^{5} + 18 x^{4} + 21 x^{3} + 18 x^{2} + 18 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.118 |
$12$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 18 x^{5} + 18 x^{3} + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 21 x^{6} + 18 x^{5} + 18 x^{3} + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.119 |
$12$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{3} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.12 |
$12$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.120 |
$12$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x^{2} + 18 x + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.121 |
$12$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{2} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.122 |
$12$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 18 x + 6$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.123 |
$12$ |
$x^{12} + 24 x^{6} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.124 |
$12$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 9 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 9 x^{5} + 9 x^{2} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.125 |
$12$ |
$x^{12} + 3 x^{9} + 6 x^{6} + 18 x^{4} + 15 x^{3} + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 6 x^{6} + 18 x^{4} + 15 x^{3} + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.126 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 18 x^{3} + 9 x^{2} + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 18 x^{3} + 9 x^{2} + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.127 |
$12$ |
$x^{12} + 6 x^{6} + 18 x^{5} + 18 x^{4} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 18 x^{5} + 18 x^{4} + 18 x + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.128 |
$12$ |
$x^{12} + 18 x^{5} + 6 x^{3} + 18 x^{2} + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 18 x^{5} + 6 x^{3} + 18 x^{2} + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.129 |
$12$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 18 x^{4} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 18 x^{4} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.13 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{5} + 18 x^{4} + 21 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{6} + 9 x^{5} + 18 x^{4} + 21 x^{3} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.130 |
$12$ |
$x^{12} + 15 x^{6} + 9 x^{5} + 18 x^{4} + 6 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 15 x^{6} + 9 x^{5} + 18 x^{4} + 6 x^{3} + 9 x^{2} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.131 |
$12$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{3} + 9 x^{2} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{3} + 9 x^{2} + 9 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.132 |
$12$ |
$x^{12} + 6 x^{6} + 18 x^{5} + 9 x^{3} + 18 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{6} + 18 x^{5} + 9 x^{3} + 18 x^{2} + 18 x + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.133 |
$12$ |
$x^{12} + 6 x^{9} + 12 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[5/4, 5/4, 2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 12 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{3} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.134 |
$12$ |
$x^{12} + 6 x^{9} + 9 x^{5} + 15 x^{3} + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 9 x^{5} + 15 x^{3} + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.135 |
$12$ |
$x^{12} + 9 x^{5} + 18 x^{4} + 9 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 9 x^{5} + 18 x^{4} + 9 x^{3} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.136 |
$12$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 9 x^{4} + 9 x^{3} + 18 x^{2} + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 9 x^{4} + 9 x^{3} + 18 x^{2} + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.137 |
$12$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 9 x^{3} + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 24 x^{6} + 18 x^{5} + 18 x^{4} + 9 x^{3} + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.138 |
$12$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 9 x^{4} + 21 x^{3} + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 6 x^{6} + 9 x^{4} + 21 x^{3} + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.139 |
$12$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 21 x^{3} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 12 x^{6} + 18 x^{5} + 21 x^{3} + 9 x + 12$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.14 |
$12$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$23$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$4$ |
$[5/2]$ |
$[5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 15 x^{6} + 9 x^{5} + 9 x^{4} + 18 x^{2} + 24$ |
$[12, 0]$ |
$[2, 2]$ |
| 3.12.23.140 |
$12$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{3} + 9 x^{2} + 21$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_6\wr C_2$ (as 12T42) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 9 x^{6} + 9 x^{5} + 9 x^{3} + 9 x^{2} + 21$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.141 |
$12$ |
$x^{12} + 6 x^{9} + 3 x^{6} + 9 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[5/2]$ |
$[2, 9/4, 9/4, 5/2]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{9} + 3 x^{6} + 9 x^{3} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.142 |
$12$ |
$x^{12} + 21 x^{6} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 21 x^{6} + 18 x^{4} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
| 3.12.23.143 |
$12$ |
$x^{12} + 3 x^{9} + 18 x^{6} + 18 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$23$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[5/2]$ |
$[9/4, 9/4, 5/2]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{9} + 18 x^{6} + 18 x^{3} + 18 x + 3$ |
$[12, 0]$ |
$[1, 2]$ |
