| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.12.24 |
$12$ |
$x^{12} - 12 x^{7} - 6 x^{6} + 72 x^{2} + 72 x + 18$ |
$3$ |
$6$ |
$2$ |
$12$ |
$C_3^4:\OD_{16}$ (as 12T215) |
$4$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.25 |
$12$ |
$x^{12} - 6 x^{7} - 6 x^{6} + 9 x^{4} + 36 x^{3} + 63 x^{2} + 54 x + 18$ |
$3$ |
$6$ |
$2$ |
$12$ |
$C_3^4:\OD_{16}$ (as 12T215) |
$4$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{2} + \left(6 t + 3\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.26 |
$12$ |
$x^{12} - 12 x^{8} + 6 x^{7} + 6 x^{6} + 72 x^{4} - 36 x^{3} - 27 x^{2} + 18 x + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\SOPlus(4,2)$ (as 12T34) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{2} + 3 x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.27 |
$12$ |
$x^{12} - 12 x^{7} + 6 x^{6} + 9 x^{4} + 36 x^{3} + 72 x^{2} - 36 x + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\PSU(3,2)$ (as 12T47) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{2} + 6 t x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.28 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 36 x^{3} + 9 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\SOPlus(4,2)$ (as 12T34) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + \left(3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.14.1 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 18 x^{4} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.10 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{8} + 51 x^{6} - 36 x^{5} + 36 x^{4} - 18 x^{3} + 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.11 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 792 x^{8} + 1728 x^{7} + 2918 x^{6} + 3684 x^{5} + 3156 x^{4} + 1376 x^{3} - 36 x^{2} - 168 x + 25$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.12 |
$12$ |
$x^{12} + 12 x^{8} - 6 x^{6} + 36 x^{4} - 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6.D_6$ (as 12T39) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.13 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 30 x^{6} - 36 x^{5} + 45 x^{4} - 36 x^{3} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.14 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 45 x^{4} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.15 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 24 x^{6} - 18 x^{5} + 9 x^{4} - 18 x^{3} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.2 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 39 x^{6} + 18 x^{5} + 18 x^{4} + 54 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + \left(3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.3 |
$12$ |
$x^{12} + 30 x^{6} + 72 x^{5} + 36 x^{4} + 36 x^{3} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.4 |
$12$ |
$x^{12} - 6 x^{9} - 12 x^{8} + 24 x^{6} + 72 x^{5} + 72 x^{4} - 18 x^{3} - 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 6 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.5 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.6 |
$12$ |
$x^{12} + 6 x^{8} + 15 x^{6} + 9 x^{4} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.7 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 42 x^{6} - 36 x^{5} + 18 x^{4} + 36 x^{3} - 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + 3 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.8 |
$12$ |
$x^{12} + 42 x^{6} + 72 x^{5} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.9 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{6} + 18 x^{5} + 9 x^{4} + 36 x^{3} + 18 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + \left(3 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.18.1 |
$12$ |
$x^{12} + 30 x^{10} + 42 x^{9} + 18 x^{8} - 18 x^{7} + 39 x^{6} + 36 x^{5} - 72 x^{4} + 90 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$2$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{5} + 3 t x^{4} + 3 x^{3} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.10 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 42 x^{9} + 54 x^{8} + 36 x^{7} - 15 x^{6} - 72 x^{5} - 144 x^{4} - 72 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 3 x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.11 |
$12$ |
$x^{12} - 12 x^{11} + 78 x^{10} - 36 x^{9} + 81 x^{8} + 30 x^{6} + 72 x^{5} - 18 x^{4} + 36 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 3 x^{4} + \left(6 t + 6\right) x^{3} + 3 t$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.12 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 18 x^{9} + 18 x^{8} + 18 x^{7} - 3 x^{6} - 36 x^{5} + 90 x^{4} + 54 x^{3} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 t x^{4} + \left(3 t + 3\right) x^{3} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.13 |
$12$ |
$x^{12} + 6 x^{11} - 3 x^{10} - 30 x^{9} + 90 x^{8} - 36 x^{7} + 21 x^{6} + 36 x^{5} + 72 x^{4} + 36 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 t x^{4} + 3 x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.14 |
$12$ |
$x^{12} - 6 x^{11} + 6 x^{10} + 72 x^{9} + 72 x^{8} + 30 x^{6} - 72 x^{5} - 144 x^{4} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + 6 t x^{4} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.15 |
$12$ |
$x^{12} + 6 x^{11} + 15 x^{10} + 24 x^{9} + 36 x^{8} + 18 x^{7} - 15 x^{6} - 72 x^{5} + 54 x^{4} - 72 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.16 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 18 x^{8} + 42 x^{6} + 126 x^{5} - 126 x^{4} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + 3 t x^{4} + 21$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.17 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 72 x^{9} + 36 x^{8} + 60 x^{6} + 144 x^{5} + 144 x^{4} + 108 x^{3} + 225$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 9 t + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.18 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 36 x^{9} + 18 x^{8} + 6 x^{6} + 72 x^{5} + 72 x^{4} + 90$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(3 t + 6\right) x^{4} + 9 t + 12$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.19 |
$12$ |
$x^{12} - 6 x^{11} + 33 x^{10} + 108 x^{9} + 108 x^{8} + 36 x^{7} + 51 x^{6} - 126 x^{5} - 252 x^{4} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[2]$ |
$[2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 t x^{4} + \left(3 t + 3\right) x^{3} + 21$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.2 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 36 x^{9} + 36 x^{8} + 39 x^{6} + 90 x^{5} + 180 x^{4} + 18 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 x^{4} + \left(3 t + 3\right) x^{3} + 3 t + 18$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.20 |
$12$ |
$x^{12} + 21 x^{10} + 6 x^{9} + 36 x^{8} + 36 x^{7} + 21 x^{6} + 72 x^{5} + 72 x^{4} + 36 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 6 x^{4} + 3 x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.21 |
$12$ |
$x^{12} - 6 x^{9} + 36 x^{8} + 36 x^{7} + 24 x^{6} - 18 x^{3} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{4} + 3 t x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.22 |
$12$ |
$x^{12} + 12 x^{11} + 36 x^{10} + 9 x^{8} - 42 x^{6} - 252 x^{5} + 126 x^{4} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 3\right) x^{4} + 21 t$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.23 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 72 x^{9} + 36 x^{8} + 42 x^{6} + 36 x^{5} + 36 x^{4} + 216 x^{3} + 333$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 18 t + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.24 |
$12$ |
$x^{12} + 6 x^{10} - 6 x^{9} + 18 x^{8} + 18 x^{7} + 69 x^{6} + 126 x^{4} + 36 x^{3} + 225$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 3\right) x^{3} + 9 t + 21$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.25 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 36 x^{9} + 45 x^{8} - 12 x^{6} - 72 x^{5} + 144 x^{4} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.26 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 48 x^{9} - 54 x^{8} + 72 x^{7} + 48 x^{6} - 144 x^{5} + 144 x^{4} + 288 x^{3} + 288$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 t x^{4} + 6 t x^{3} + 12 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.27 |
$12$ |
$x^{12} - 6 x^{11} + 24 x^{10} - 12 x^{9} + 90 x^{8} + 84 x^{6} + 36 x^{5} + 108 x^{4} + 72 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + \left(3 t + 6\right) x^{4} + 6 t x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.28 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 12 x^{9} + 27 x^{8} - 18 x^{7} + 51 x^{6} + 18 x^{5} + 18 x^{4} - 18 x^{3} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + 3 x^{4} + \left(6 t + 3\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.29 |
$12$ |
$x^{12} - 12 x^{10} - 6 x^{9} + 72 x^{8} + 108 x^{7} + 57 x^{6} + 72 x^{4} + 108 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{4} + \left(6 t + 3\right) x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.3 |
$12$ |
$x^{12} - 6 x^{11} + 39 x^{10} + 90 x^{9} + 45 x^{8} - 12 x^{6} + 144 x^{5} + 144 x^{4} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + \left(6 t + 3\right) x^{4} + 9 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.30 |
$12$ |
$x^{12} + 9 x^{10} + 30 x^{9} + 72 x^{8} + 72 x^{7} + 87 x^{6} - 126 x^{3} + 441$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_2^2$ (as 12T130) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + \left(6 t + 6\right) x^{4} + \left(6 t + 3\right) x^{3} + 21$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.31 |
$12$ |
$x^{12} - 12 x^{11} + 84 x^{10} - 72 x^{9} + 108 x^{8} + 42 x^{6} - 36 x^{5} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 6 x^{4} + \left(6 t + 6\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.32 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 18 x^{9} + 45 x^{8} + 36 x^{7} + 3 x^{6} - 18 x^{5} + 54 x^{4} + 18 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(6 t + 3\right) x^{4} + \left(3 t + 3\right) x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.33 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 30 x^{9} - 18 x^{8} + 72 x^{7} + 66 x^{6} - 18 x^{5} + 36 x^{4} + 72 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 t x^{4} + 6 t x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.34 |
$12$ |
$x^{12} + 6 x^{10} + 18 x^{8} + 36 x^{7} + 6 x^{6} + 18 x^{4} + 216 x^{3} + 549$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^4:(C_2\times C_4)$ (as 12T171) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{4} + \left(6 t + 6\right) x^{3} + 18 t + 3$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.35 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 30 x^{9} + 18 x^{8} - 36 x^{7} + 6 x^{6} - 36 x^{5} - 72 x^{4} + 144 x^{3} + 360$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 x^{4} + 3 t x^{3} + 18 t + 12$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.36 |
$12$ |
$x^{12} - 6 x^{11} + 57 x^{10} - 42 x^{9} + 126 x^{8} - 36 x^{7} + 51 x^{6} - 18 x^{5} + 36 x^{4} - 18 x^{3} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_6\times S_3$ (as 12T18) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 x^{4} + \left(6 t + 3\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
