| 3.12.0.1 |
x12 - x4 - x3 - x2 + x - 1 |
3 |
1 |
12 |
0 |
$C_{12}$ (as 12T1) |
$ [\ ]^{12}$ |
| 3.12.6.1 |
x12 - 243x2 + 1458 |
3 |
2 |
6 |
6 |
$C_{12}$ (as 12T1) |
$ [\ ]_{2}^{6}$ |
| 3.12.6.2 |
x12 + 108x6 - 243x2 + 2916 |
3 |
2 |
6 |
6 |
$C_6\times C_2$ (as 12T2) |
$ [\ ]_{2}^{6}$ |
| 3.12.9.1 |
x12 - 6x8 + 9x4 - 27 |
3 |
4 |
3 |
9 |
$D_4 \times C_3$ (as 12T14) |
$ [\ ]_{4}^{6}$ |
| 3.12.9.2 |
x12 - 9x4 + 27 |
3 |
4 |
3 |
9 |
$D_4 \times C_3$ (as 12T14) |
$ [\ ]_{4}^{6}$ |
| 3.12.12.1 |
x12 + 27x6 + 81x5 - 54x3 - 81x - 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.10 |
x12 + 9x11 + 36x10 - 72x9 + 18x8 + 45x7 + 99x6 + 54x5 + 81x4 - 81x3 + 81x2 - 81x + 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.11 |
x12 + 18x11 - 120x10 - 33x9 - 99x8 - 117x7 + 108x6 + 54x4 - 81x2 - 81x - 81 |
3 |
3 |
4 |
12 |
12T170 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.12 |
x12 + 165x10 - 312x9 - 288x8 - 180x7 - 36x6 - 135x5 - 243x4 + 54x3 + 81x2 + 81x - 162 |
3 |
3 |
4 |
12 |
$C_2\times C_3:S_3.C_2$ (as 12T41) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.12.13 |
x12 + 42x11 - 57x10 - 36x9 - 117x8 - 54x7 - 18x6 - 27x5 + 54x4 + 108x3 - 81x2 + 81x + 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.14 |
x12 + 48x10 + 96x9 + 36x8 + 99x7 - 99x6 + 81x4 - 27x3 - 81x + 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.15 |
x12 + 12x11 + 87x10 + 57x9 + 81x8 - 36x6 + 54x5 + 54x4 + 54x3 - 81x - 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.16 |
x12 + 24x11 + 42x10 - 39x9 - 99x8 + 18x7 - 27x6 - 54x4 + 27x3 - 81x + 81 |
3 |
3 |
4 |
12 |
12T170 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.17 |
x12 + 12x11 - 120x10 + 108x9 + 90x8 + 99x7 + 90x6 - 27x5 + 54x4 + 81x3 - 81x2 - 81 |
3 |
3 |
4 |
12 |
12T170 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.18 |
x12 + 42x11 - 48x10 - 114x9 - 99x8 - 54x7 - 90x6 - 108x5 + 27x4 - 27x3 + 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
$F_9$ (as 12T46) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.12.19 |
x12 + 33x11 - 9x10 - 18x9 - 18x8 + 81x7 - 63x6 + 108x5 - 54x4 + 81x3 + 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
$S_3\times C_3:S_3.C_2$ (as 12T119) |
$ [3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.2 |
x12 + 78x10 - 75x9 - 36x8 + 36x7 + 81x6 - 81x5 - 81x4 + 81x3 + 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.20 |
x12 + 33x11 + 81x10 - 75x9 - 81x8 + 81x7 - 54x6 + 54x5 + 81x4 + 81x3 + 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.21 |
x12 + 12x11 + 108x10 + 108x9 - 72x8 - 99x7 - 72x6 - 108x5 - 27x4 + 108x3 + 81x + 81 |
3 |
3 |
4 |
12 |
12T173 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.22 |
x12 + 18x11 + 21x10 - 69x9 - 81x8 + 72x7 - 90x6 - 108x5 + 54x4 - 108x3 - 81 |
3 |
3 |
4 |
12 |
$S_3\times C_3:S_3.C_2$ (as 12T119) |
$ [3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.23 |
x12 + 21x11 + 21x10 + 63x9 + 36x8 + 54x7 + 90x6 + 81x3 - 81 |
3 |
3 |
4 |
12 |
$S_3 \times C_4$ (as 12T11) |
$ [3/2]_{2}^{4}$ |
| 3.12.12.24 |
x12 + 3x7 + 3x6 - 9x2 + 9x - 9 |
3 |
6 |
2 |
12 |
12T215 |
$ [5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
| 3.12.12.25 |
x12 + 3x11 + 6x10 + 6x9 + 9x8 - 3x7 + 3x6 - 9x5 + 9x2 - 9 |
3 |
6 |
2 |
12 |
12T215 |
$ [5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
| 3.12.12.26 |
x12 - 9x11 - 6x10 + 6x9 - 12x8 + 12x7 - 12x6 + 9x4 + 9x + 9 |
3 |
6 |
2 |
12 |
$S_3\wr C_2$ (as 12T34) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.12.27 |
x12 - 12x11 + 3x10 - 9x9 + 3x8 + 3x7 + 6x6 + 9x3 + 9x + 9 |
3 |
6 |
2 |
12 |
$PSU(3,2)$ (as 12T47) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.12.28 |
x12 + 12x11 - 3x10 + 3x9 + 3x8 + 6x7 + 12x6 + 9x5 + 9x4 + 9x + 9 |
3 |
6 |
2 |
12 |
$S_3\wr C_2$ (as 12T34) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.12.29 |
x12 + 3x + 3 |
3 |
12 |
1 |
12 |
$PSU(3,2):C_2$ (as 12T84) |
$ [9/8, 9/8]_{8}^{2}$ |
| 3.12.12.3 |
x12 + 42x10 - 87x9 + 90x8 - 99x7 - 72x6 - 54x5 - 27x4 - 108x3 - 81 |
3 |
3 |
4 |
12 |
12T170 |
$ [3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.30 |
x12 - 3x10 + 3x7 + 3x5 + 3x4 + 3x3 + 3x2 - 3x - 3 |
3 |
12 |
1 |
12 |
$PSU(3,2):C_2$ (as 12T84) |
$ [9/8, 9/8]_{8}^{2}$ |
| 3.12.12.4 |
x12 + 33x11 - 24x10 + 66x9 - 45x8 + 99x7 - 99x6 + 81x5 + 27x4 + 27x3 + 81x2 + 81 |
3 |
3 |
4 |
12 |
$F_9$ (as 12T46) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.12.5 |
x12 + 33x11 - 63x10 - 36x9 - 90x8 - 54x7 - 54x6 - 108x4 - 27x3 - 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
$S_3 \times C_4$ (as 12T11) |
$ [3/2]_{2}^{4}$ |
| 3.12.12.6 |
x12 + 24x11 - 3x10 + 81x9 - 18x8 + 54x7 + 108x5 - 54x4 - 27x3 - 81x - 81 |
3 |
3 |
4 |
12 |
$C_2.S_3^2$ (as 12T39) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.12.7 |
x12 + 12x11 + 108x10 + 105x9 - 45x8 + 45x7 - 81x6 - 108x5 + 27x4 - 81x3 - 81x2 + 81x - 81 |
3 |
3 |
4 |
12 |
$S_3\times C_3:S_3.C_2$ (as 12T119) |
$ [3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.8 |
x12 + 21x11 + 81x10 - 78x9 - 63x8 - 99x7 + 117x6 - 54x5 - 54x4 + 81x2 - 81x + 81 |
3 |
3 |
4 |
12 |
$S_3\times C_3:S_3.C_2$ (as 12T119) |
$ [3/2, 3/2, 3/2]_{2}^{4}$ |
| 3.12.12.9 |
x12 + 24x11 + 21x10 + 21x9 + 63x8 - 54x7 + 81x5 - 54x4 - 27x3 - 81x2 - 81x + 81 |
3 |
3 |
4 |
12 |
$C_2\times C_3:S_3.C_2$ (as 12T41) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.13.1 |
x12 + 3x2 + 3 |
3 |
12 |
1 |
13 |
$S_3\wr C_2$ (as 12T36) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.13.2 |
x12 - 3x10 + 3x6 + 3x5 - 3x3 - 3x2 + 3 |
3 |
12 |
1 |
13 |
$C_3\times S_3\wr C_2$ (as 12T121) |
$ [5/4, 5/4]_{4}^{6}$ |
| 3.12.13.3 |
x12 + 3x10 + 3x9 + 3x8 + 3x7 + 3x3 + 3x2 - 3 |
3 |
12 |
1 |
13 |
$C_3\times S_3\wr C_2$ (as 12T121) |
$ [5/4, 5/4]_{4}^{6}$ |
| 3.12.13.4 |
x12 - 3x10 + 3x6 - 3x5 + 3x4 - 3x2 - 3 |
3 |
12 |
1 |
13 |
$S_3\wr C_2$ (as 12T36) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.13.5 |
x12 + 3x11 + 3x9 - 3x8 + 3x6 - 3x2 + 3 |
3 |
12 |
1 |
13 |
$S_3\wr C_2$ (as 12T35) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.13.6 |
x12 + 3x11 + 3x7 + 3x6 + 3x4 + 3x2 - 3 |
3 |
12 |
1 |
13 |
$S_3\wr C_2$ (as 12T35) |
$ [5/4, 5/4]_{4}^{2}$ |
| 3.12.14.1 |
x12 + 3x8 + 3x6 - 9x4 + 9x2 - 9 |
3 |
6 |
2 |
14 |
$(C_3\times C_3):C_4$ (as 12T17) |
$ [3/2, 3/2]_{2}^{2}$ |
| 3.12.14.10 |
x12 - 9x11 + 9x10 + 9x9 - 12x8 - 9x5 + 9x4 + 9x3 + 9 |
3 |
6 |
2 |
14 |
$C_6\times S_3$ (as 12T18) |
$ [3/2]_{2}^{6}$ |
| 3.12.14.11 |
x12 + 6x11 + 21x10 + 36x9 + 30x8 + 36x7 + 3x6 + 36x5 + 27x4 - 9x2 + 36 |
3 |
6 |
2 |
14 |
$D_6$ (as 12T3) |
$ [3/2]_{2}^{2}$ |
| 3.12.14.12 |
x12 + 9x11 + 9x10 + 12x8 + 12x6 + 9x5 + 9x4 - 9x2 - 9 |
3 |
6 |
2 |
14 |
$C_2.S_3^2$ (as 12T39) |
$ [3/2, 3/2]_{2}^{4}$ |
| 3.12.14.13 |
x12 + 9x11 - 9x10 - 3x9 - 6x8 + 9x7 - 6x6 + 9x4 + 9x3 - 9 |
3 |
6 |
2 |
14 |
$C_3\times C_3:S_3.C_2$ (as 12T73) |
$ [3/2, 3/2]_{2}^{6}$ |
| 3.12.14.14 |
x12 - 12x11 - 3x10 - 6x8 + 3x6 - 9x5 - 9x4 - 9 |
3 |
6 |
2 |
14 |
$(C_3\times C_3):C_4$ (as 12T17) |
$ [3/2, 3/2]_{2}^{2}$ |
| 3.12.14.15 |
x12 + 9x11 - 6x10 + 6x9 - 3x8 + 9x7 + 6x6 - 9x5 - 9x4 - 9x3 - 9x2 + 9 |
3 |
6 |
2 |
14 |
$C_6\times S_3$ (as 12T18) |
$ [3/2]_{2}^{6}$ |
| 3.12.14.2 |
x12 + 12x11 - 6x10 + 6x9 - 12x8 + 12x6 - 9x4 - 9 |
3 |
6 |
2 |
14 |
$C_3\times C_3:S_3.C_2$ (as 12T73) |
$ [3/2, 3/2]_{2}^{6}$ |
| 3.12.14.3 |
x12 - 12x11 + 3x10 - 9x7 - 6x6 - 9x3 + 9x2 - 9 |
3 |
6 |
2 |
14 |
$S_3 \times C_4$ (as 12T11) |
$ [3/2]_{2}^{4}$ |
