| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.0.1 |
$12$ |
$x^{12} + x^{7} + x^{6} + x^{5} + x^{3} + x + 1$ |
$2$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{7} + t^{6} + t^{5} + t^{3} + t + 1$ |
$x - 2$ |
$[0]$ |
$[]$ |
| 2.12.8.1 |
$12$ |
$x^{12} + 11 x^{9} + 3 x^{8} - 9 x^{6} - 90 x^{5} + 3 x^{4} - 27 x^{3} + 135 x^{2} + 27 x + 55$ |
$2$ |
$3$ |
$4$ |
$8$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{4}$ |
$t^{4} + t + 1$ |
$x^{3} + 2$ |
$[0]$ |
$[1]$ |
| 2.12.8.2 |
$12$ |
$x^{12} - 8 x^{3} + 16$ |
$2$ |
$3$ |
$4$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$t^{4} + t + 1$ |
$x^{3} + 2 t$ |
$[0]$ |
$[1]$ |
| 2.12.12.1 |
$12$ |
$x^{12} + 16 x^{11} + 100 x^{10} + 184 x^{9} + 44 x^{8} - 1472 x^{7} - 2336 x^{6} - 1600 x^{5} + 18032 x^{4} + 37504 x^{3} + 66880 x^{2} + 40064 x + 13120$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{4} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.10 |
$12$ |
$x^{12} + 8 x^{11} + 32 x^{10} + 120 x^{9} + 356 x^{8} + 16 x^{7} - 1312 x^{6} - 3936 x^{5} - 17296 x^{4} - 14272 x^{3} + 103296 x^{2} + 36352 x + 38848$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.11 |
$12$ |
$x^{12} + 28 x^{10} + 40 x^{9} + 356 x^{8} + 896 x^{7} + 2720 x^{6} + 6656 x^{5} + 12464 x^{4} + 19456 x^{3} + 26304 x^{2} + 19840 x + 5824$ |
$2$ |
$2$ |
$6$ |
$12$ |
$A_4 \times C_2$ (as 12T7) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.12 |
$12$ |
$x^{12} + 84 x^{10} - 88 x^{9} + 1660 x^{8} - 1568 x^{7} + 13920 x^{6} - 4928 x^{5} + 47280 x^{4} + 23936 x^{3} + 63552 x^{2} + 32896 x + 51520$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.13 |
$12$ |
$x^{12} - 6 x^{11} + 60 x^{10} - 100 x^{9} + 876 x^{8} - 304 x^{7} + 5696 x^{6} + 544 x^{5} + 17712 x^{4} - 1248 x^{3} + 14144 x^{2} - 5184 x + 1600$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.14 |
$12$ |
$x^{12} - 6 x^{11} + 36 x^{10} - 164 x^{9} + 660 x^{8} - 2352 x^{7} + 6720 x^{6} - 15584 x^{5} + 28656 x^{4} - 41056 x^{3} + 48320 x^{2} - 37696 x + 22720$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.15 |
$12$ |
$x^{12} - 4 x^{11} + 44 x^{10} - 152 x^{9} + 692 x^{8} - 1952 x^{7} + 6624 x^{6} - 12224 x^{5} + 33776 x^{4} - 54976 x^{3} + 73920 x^{2} - 129664 x + 96448$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.16 |
$12$ |
$x^{12} - 6 x^{11} + 16 x^{10} - 12 x^{9} - 68 x^{8} + 16 x^{7} + 832 x^{6} - 4320 x^{5} + 11632 x^{4} - 6240 x^{3} + 13568 x^{2} + 9536 x + 1600$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.17 |
$12$ |
$x^{12} + 12 x^{10} + 32 x^{9} + 84 x^{8} + 32 x^{7} + 544 x^{6} - 704 x^{5} - 4176 x^{4} - 5248 x^{3} + 16064 x^{2} + 21248 x + 6592$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$12$ |
$1$ |
$[2]$ |
$[2, 2]^{12}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.18 |
$12$ |
$x^{12} - 10 x^{11} + 72 x^{10} - 332 x^{9} + 1316 x^{8} - 4160 x^{7} + 12128 x^{6} - 27904 x^{5} + 53744 x^{4} - 69600 x^{3} + 71680 x^{2} - 41536 x + 38848$ |
$2$ |
$2$ |
$6$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.19 |
$12$ |
$x^{12} + 6 x^{11} + 40 x^{10} + 188 x^{9} + 732 x^{8} + 2896 x^{7} + 8224 x^{6} + 22240 x^{5} + 43760 x^{4} + 56672 x^{3} + 77824 x^{2} - 19776 x + 66112$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{12}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{5} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.2 |
$12$ |
$x^{12} - 2 x^{11} - 8 x^{10} - 244 x^{9} + 500 x^{8} + 1696 x^{7} + 6656 x^{6} + 22336 x^{5} + 35952 x^{4} + 61344 x^{3} + 75648 x^{2} + 52288 x + 36544$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.20 |
$12$ |
$x^{12} - 2 x^{11} - 172 x^{9} - 172 x^{8} + 2112 x^{7} + 7968 x^{6} + 13568 x^{5} + 22320 x^{4} + 29216 x^{3} + 22912 x^{2} + 18624 x + 11200$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.21 |
$12$ |
$x^{12} + 16 x^{11} + 88 x^{10} + 24 x^{9} - 1308 x^{8} - 4288 x^{7} - 736 x^{6} + 26176 x^{5} + 68592 x^{4} + 77696 x^{3} + 42752 x^{2} + 13440 x + 4544$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.22 |
$12$ |
$x^{12} + 10 x^{11} - 16 x^{10} - 316 x^{9} - 364 x^{8} + 1040 x^{7} + 7648 x^{6} + 17632 x^{5} + 25008 x^{4} + 17056 x^{3} + 6016 x^{2} + 1344 x + 4544$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{5} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.23 |
$12$ |
$x^{12} + 56 x^{10} - 152 x^{9} - 764 x^{8} + 2976 x^{7} - 960 x^{6} - 11008 x^{5} + 20336 x^{4} - 14976 x^{3} + 80768 x^{2} + 6016 x + 38848$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.24 |
$12$ |
$x^{12} - 10 x^{11} + 72 x^{10} - 292 x^{9} + 1028 x^{8} - 2144 x^{7} + 5280 x^{6} - 5568 x^{5} + 12400 x^{4} - 12384 x^{3} + 24832 x^{2} - 14784 x + 11200$ |
$2$ |
$2$ |
$6$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.25 |
$12$ |
$x^{12} + 12 x^{11} + 60 x^{10} + 160 x^{9} + 308 x^{8} + 736 x^{7} + 2272 x^{6} + 5632 x^{5} + 10608 x^{4} + 15040 x^{3} + 12224 x^{2} + 3584 x + 704$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.26 |
$12$ |
$x^{12} + 12 x^{11} + 98 x^{10} + 542 x^{9} + 2359 x^{8} + 7956 x^{7} + 21831 x^{6} + 47308 x^{5} + 82476 x^{4} + 109442 x^{3} + 112071 x^{2} + 76900 x + 33205$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.27 |
$12$ |
$x^{12} + 4 x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{4} - 4 x^{3} + 12 x^{2} - 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3]_{3}^{4}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + 2 t x + 2$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.12.28 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 50 x^{9} + 90 x^{8} + 130 x^{7} + 159 x^{6} + 132 x^{5} + 10 x^{4} - 100 x^{3} - 53 x^{2} + 22 x + 19$ |
$2$ |
$6$ |
$2$ |
$12$ |
$S_4$ (as 12T9) |
$2$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x + 2$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.12.29 |
$12$ |
$x^{12} + 4 x^{8} + 4 x^{7} - 2 x^{6} + 4 x^{4} + 8 x^{3} - 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{12}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + 2 x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.12.3 |
$12$ |
$x^{12} - 4 x^{11} + 52 x^{10} - 128 x^{9} + 532 x^{8} - 1184 x^{7} + 6080 x^{6} - 2304 x^{5} + 36144 x^{4} - 10688 x^{3} + 86208 x^{2} - 38656 x + 107968$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.30 |
$12$ |
$x^{12} + 4 x^{8} + 2 x^{7} - 2 x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 4$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + \left(2 t + 2\right) x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 2.12.12.31 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 6 x^{8} + 12 x^{7} + 32 x^{6} + 48 x^{5} + 76 x^{4} + 48 x^{3} + 40 x^{2} + 8 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_2^4:(C_3\times S_4)$ (as 12T205) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.12.32 |
$12$ |
$x^{12} - 4 x^{10} - 4 x^{9} + 26 x^{8} + 40 x^{7} - 4 x^{6} - 40 x^{5} + 28 x^{4} + 72 x^{3} + 24 x^{2} - 16 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$A_4\wr C_2$ (as 12T129) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{2} + \left(2 t^{2} + 2 t\right) x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.12.33 |
$12$ |
$x^{12} + 2 x^{10} + 6 x^{9} + 6 x^{8} + 8 x^{7} + 28 x^{6} + 24 x^{5} + 20 x^{4} + 24 x^{3} + 32 x^{2} + 24 x + 8$ |
$2$ |
$4$ |
$3$ |
$12$ |
$C_3\times S_4$ (as 12T45) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3]_{3}^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2\right) x^{2} + 2 x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
| 2.12.12.34 |
$12$ |
$x^{12} + 2 x + 2$ |
$2$ |
$12$ |
$1$ |
$12$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[10/9, 10/9]$ |
$[10/9, 10/9, 10/9, 10/9, 10/9, 10/9]_{9}^{6}$ |
$t + 1$ |
$x^{12} + 2 x + 2$ |
$[1, 1, 0]$ |
$[1, 2]$ |
| 2.12.12.4 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 84 x^{9} + 196 x^{8} + 336 x^{7} + 768 x^{6} + 2144 x^{5} + 4784 x^{4} + 8032 x^{3} + 9600 x^{2} + 6976 x + 2240$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t + 2\right) x + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.5 |
$12$ |
$x^{12} + 4 x^{11} + 24 x^{10} - 8 x^{9} + 140 x^{8} - 1488 x^{7} + 832 x^{6} - 10208 x^{5} + 20336 x^{4} + 12160 x^{3} + 113280 x^{2} + 139520 x + 45376$ |
$2$ |
$2$ |
$6$ |
$12$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 t^{4} x + 4 t^{5} + 4 t^{4} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.6 |
$12$ |
$x^{12} + 16 x^{11} + 120 x^{10} - 1052 x^{8} - 1904 x^{7} - 736 x^{6} + 3104 x^{5} + 15856 x^{4} + 18368 x^{3} + 28160 x^{2} + 14208 x + 11200$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{12}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.7 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{10} + 108 x^{9} + 452 x^{8} + 1328 x^{7} + 5952 x^{6} + 25760 x^{5} + 72688 x^{4} + 129184 x^{3} + 143232 x^{2} + 92096 x + 26560$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.8 |
$12$ |
$x^{12} - 4 x^{11} + 20 x^{10} - 64 x^{9} + 196 x^{8} - 336 x^{7} + 736 x^{6} + 160 x^{5} + 1712 x^{4} + 5632 x^{3} + 5440 x^{2} + 6784 x + 5824$ |
$2$ |
$2$ |
$6$ |
$12$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 t^{2} x + 4 t^{5} + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.9 |
$12$ |
$x^{12} + 2 x^{11} + 52 x^{10} + 116 x^{9} + 964 x^{8} + 2928 x^{7} + 10272 x^{6} + 24800 x^{5} + 47088 x^{4} + 67104 x^{3} + 107584 x^{2} + 64320 x + 107968$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.14.1 |
$12$ |
$x^{12} + 2 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$14$ |
$S_4$ (as 12T8) |
$2$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3]_{3}^{2}$ |
$t + 1$ |
$x^{12} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2, 2]$ |
| 2.12.14.2 |
$12$ |
$x^{12} + 2 x^{4} + 2 x^{3} + 2$ |
$2$ |
$12$ |
$1$ |
$14$ |
$A_4:C_4$ (as 12T27) |
$4$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3]_{3}^{4}$ |
$t + 1$ |
$x^{12} + 2 x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2, 2]$ |
| 2.12.14.3 |
$12$ |
$x^{12} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$12$ |
$1$ |
$14$ |
$A_4\wr C_2$ (as 12T128) |
$6$ |
$3$ |
$[4/3, 4/3]$ |
$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
$t + 1$ |
$x^{12} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 0]$ |
$[3, 2]$ |
| 2.12.16.1 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 4 x^{9} - 4 x^{7} + 10 x^{6} + 8 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.10 |
$12$ |
$x^{12} - 2 x^{11} + 8 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 2 x^{6} + 8 x^{5} - 4 x^{4} + 4 x^{3} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{4} + \left(2 t + 2\right) x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.11 |
$12$ |
$x^{12} + 4 x^{11} + 4 x^{10} + 2 x^{9} + 8 x^{8} + 8 x^{7} + 6 x^{6} + 8 x^{5} + 4 x^{4} + 20 x^{3} + 4 x^{2} + 28$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$3$ |
$[2]$ |
$[2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t + 2\right) x^{3} + 2 x^{2} + 6 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.12 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} + 2 x^{9} + 8 x^{8} - 4 x^{7} + 10 x^{6} + 4 x^{5} + 4 x^{4} + 12 x^{3} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t + 2\right) x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.13 |
$12$ |
$x^{12} + 10 x^{11} + 47 x^{10} + 144 x^{9} + 330 x^{8} + 578 x^{7} + 785 x^{6} + 830 x^{5} + 530 x^{4} - 64 x^{3} - 189 x^{2} - 30 x + 25$ |
$2$ |
$6$ |
$2$ |
$16$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.14 |
$12$ |
$x^{12} - 2 x^{11} + 4 x^{10} - 2 x^{9} + 12 x^{8} - 4 x^{7} + 10 x^{6} - 4 x^{5} + 4 x^{4} + 12 x^{2} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t x^{3} + 2 x^{2} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.15 |
$12$ |
$x^{12} + 2 x^{10} - 2 x^{9} + 8 x^{8} + 4 x^{7} + 12 x^{6} - 4 x^{5} + 8 x^{4} - 4 x^{3} + 8 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{4} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.16 |
$12$ |
$x^{12} + 4 x^{11} + 8 x^{10} + 12 x^{9} + 16 x^{8} + 16 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.17 |
$12$ |
$x^{12} - 2 x^{10} - 2 x^{9} + 8 x^{8} + 8 x^{7} - 2 x^{6} - 4 x^{5} + 12 x^{4} + 8 x^{3} - 4 x^{2} + 4$ |
$2$ |
$6$ |
$2$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{4} + 2 t x^{3} + 2 x^{2} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
| 2.12.16.18 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{7} + 12 x^{6} + 8 x^{5} + 4 x^{4} + 12$ |
$2$ |
$6$ |
$2$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[2]$ |
$[2]_{3}^{2}$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
