| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.21.1 |
$12$ |
$x^{12} + 3 x^{10} + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 3$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.10 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.100 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{6} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{6} + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.101 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{2} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{2} + 9 x + 12$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.102 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 21$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.103 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.104 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 9 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 9 x^{3} + 9 x^{2} + 6$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.105 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 18 x + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.106 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 15 x^{3} + 18 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 15 x^{3} + 18 x + 12$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.107 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{6} + 18 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{6} + 18 x^{3} + 9 x + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.108 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 3 x^{3} + 18 x + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.109 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{3} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{3} + 18 x + 3$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.11 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{6} + 6 x^{3} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{6} + 6 x^{3} + 18 x + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.110 |
$12$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 9 x^{3} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 9 x^{3} + 18 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.111 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.112 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 9 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 9 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.113 |
$12$ |
$x^{12} + 6 x^{10} + 3 x^{6} + 9 x^{2} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3 x^{6} + 9 x^{2} + 18 x + 6$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.114 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 6$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.12 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{3} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{3} + 18 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.13 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.14 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 9 x^{3} + 9 x + 12$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.15 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.16 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x^{2} + 18 x + 21$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.17 |
$12$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 3 x^{6} + 3 x^{3} + 18 x^{2} + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.18 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 6 x^{6} + 24 x^{3} + 9 x^{2} + 9 x + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.19 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.2 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 9 x + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.20 |
$12$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 9 x^{2} + 9 x + 21$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.21 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 3 x^{3} + 18 x^{2} + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 3 x^{3} + 18 x^{2} + 12$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.22 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 6 x^{6} + 9 x^{3} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{9} + 6 x^{6} + 9 x^{3} + 18 x^{2} + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.23 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 15 x^{3} + 18 x^{2} + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{6} + 15 x^{3} + 18 x^{2} + 12$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.24 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{6} + 18 x^{2} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{6} + 18 x^{2} + 9 x + 21$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.25 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 9 x^{3} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 3 x^{6} + 9 x^{3} + 18 x + 21$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.26 |
$12$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.27 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 9 x^{3} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{9} + 9 x^{3} + 18 x + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.28 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.29 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{6} + 12 x^{3} + 9 x^{2} + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{6} + 12 x^{3} + 9 x^{2} + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.3 |
$12$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 21 x^{3} + 9 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3 x^{9} + 21 x^{3} + 9 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.30 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 18 x + 15$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.31 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.32 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 6 x^{3} + 9 x^{2} + 18 x + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 6 x^{6} + 6 x^{3} + 9 x^{2} + 18 x + 24$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.33 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 9 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.34 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{2} + 9 x + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.35 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 3$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 3$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.36 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 24$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[9/4]$ |
$[2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{6} + 24 x^{3} + 18 x^{2} + 24$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.37 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{2} + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{2} + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.38 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{2} + 18 x + 21$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 6 x^{6} + 9 x^{2} + 18 x + 21$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.39 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{3} + 15$ |
$3$ |
$12$ |
$1$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{6} + 18 x^{3} + 15$ |
$[10, 0]$ |
$[1, 2]$ |
| 3.12.21.4 |
$12$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[9/4]$ |
$[9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 3 x^{6} + 18 x^{3} + 9 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
| 3.12.21.40 |
$12$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 12$ |
$3$ |
$12$ |
$1$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[9/4]$ |
$[3/2, 9/4, 9/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6 x^{6} + 18 x^{3} + 18 x^{2} + 18 x + 12$ |
$[10, 0]$ |
$[1, 2]$ |
