| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.12.11 |
$12$ |
$x^{12} - 48 x^{11} + 846 x^{10} - 5820 x^{9} + 38376 x^{8} + 37098 x^{7} - 36666 x^{6} - 17928 x^{5} + 11340 x^{4} - 1188 x^{3} + 486 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t\right) x^{2} + \left(6 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.16 |
$12$ |
$x^{12} - 18 x^{11} + 30 x^{10} + 1020 x^{9} + 3249 x^{8} + 6480 x^{7} + 21924 x^{6} + 35208 x^{5} + 7452 x^{4} - 8478 x^{3} + 5670 x^{2} - 1134 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.17 |
$12$ |
$x^{12} + 36 x^{11} + 540 x^{10} + 3900 x^{9} + 8028 x^{8} - 44388 x^{7} + 21870 x^{6} + 7020 x^{5} + 20412 x^{4} - 8316 x^{3} + 4212 x^{2} - 972 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{3} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.3 |
$12$ |
$x^{12} + 6 x^{11} + 60 x^{10} + 210 x^{9} + 1170 x^{8} + 2322 x^{7} + 1782 x^{6} + 6048 x^{5} + 13527 x^{4} + 8370 x^{3} + 2916 x^{2} + 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 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) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 3 x^{4} + \left(6 t + 6\right) x^{3} + 3 t$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.2 |
$12$ |
$x^{12} + 6 x^{11} + 21 x^{10} + 36 x^{9} + 36 x^{8} + 39 x^{6} + 90 x^{5} + 180 x^{4} + 18 x^{3} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:(C_4\times S_3)$ (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) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 6 x^{4} + 3 x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.18.8 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 36 x^{9} + 9 x^{8} - 42 x^{6} - 252 x^{5} - 126 x^{4} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 x^{4} + 21 t$ |
$[4, 0]$ |
$[2, 1]$ |
| 3.12.20.11 |
$12$ |
$x^{12} - 18 x^{11} + 288 x^{10} - 3642 x^{9} + 66825 x^{8} + 489564 x^{7} + 1863378 x^{6} + 4339494 x^{5} + 6999615 x^{4} + 7773678 x^{3} + 5967108 x^{2} + 2842128 x + 737586$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{3} + 9 t^{2} + 9 t + 9\right) x^{2} + \left(9 t^{3} + 9 t^{2} + 18 t + 9\right) x + 18 t^{3} + 9 t^{2} + 9 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.12 |
$12$ |
$x^{12} - 180 x^{11} + 10404 x^{10} - 121398 x^{9} + 2903202 x^{8} - 678618 x^{7} + 1727460 x^{6} + 3247938 x^{5} + 4136589 x^{4} - 3041280 x^{3} - 3189132 x^{2} + 696438 x + 578421$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(18 t^{3} + 18 t\right) x^{2} + 9 x + 9 t^{2} + 9 t + 21$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.13 |
$12$ |
$x^{12} + 72 x^{11} + 2160 x^{10} + 23178 x^{9} - 36774 x^{8} - 1448118 x^{7} + 1360692 x^{6} + 12416814 x^{5} + 18786573 x^{4} + 15404364 x^{3} + 9738468 x^{2} + 4293810 x + 842805$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{2} + 18 t + 18\right) x^{2} + \left(18 t^{3} + 9 t^{2} + 18 t + 9\right) x + 18 t^{3} + 9 t + 3$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.14 |
$12$ |
$x^{12} - 36 x^{11} + 648 x^{10} - 5100 x^{9} + 12960 x^{8} + 120528 x^{7} + 117180 x^{6} - 46656 x^{5} + 104976 x^{4} + 263520 x^{3} + 188568 x^{2} + 244944 x + 155844$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{3} + 9 t^{2}\right) x^{2} + \left(18 t^{3} + 18 t^{2} + 18\right) x + 9 t^{2} + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.15 |
$12$ |
$x^{12} + 54 x^{10} + 12 x^{9} + 972 x^{8} + 5400 x^{6} - 11664 x^{5} - 10206 x^{4} - 43632 x^{3} + 34992 x^{2} + 233280 x + 168480$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t + 18\right) x + 18 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.17 |
$12$ |
$x^{12} - 108 x^{10} - 12012 x^{9} + 420714 x^{8} + 3115908 x^{7} + 8387604 x^{6} + 11429748 x^{5} + 9035469 x^{4} + 4043628 x^{3} + 1043928 x^{2} + 169128 x + 18792$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{3} + 9 t^{2} + 18 t + 18\right) x^{2} + \left(18 t^{3} + 9 t^{2} + 18 t + 9\right) x + 9 t^{3} + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.18 |
$12$ |
$x^{12} - 90 x^{11} + 3798 x^{10} - 81024 x^{9} + 925830 x^{8} + 3175200 x^{7} + 5644296 x^{6} + 6774840 x^{5} + 6191154 x^{4} + 3846312 x^{3} + 1990656 x^{2} + 544320 x + 129600$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(18 t^{3} + 18 t^{2} + 9 t\right) x^{2} + \left(9 t^{3} + 9 t\right) x + 18 t^{3} + 18 t^{2} + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.19 |
$12$ |
$x^{12} + 36 x^{11} + 882 x^{10} + 5574 x^{9} + 57429 x^{8} + 202500 x^{7} + 912600 x^{6} + 1587276 x^{5} + 2101707 x^{4} + 1960146 x^{3} + 1260684 x^{2} + 602640 x + 146610$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{2} + 18 t + 9\right) x^{2} + \left(9 t^{2} + 9\right) x + 9 t^{2} + 9 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.3 |
$12$ |
$x^{12} + 522 x^{10} + 1488 x^{9} + 71280 x^{8} + 446634 x^{7} + 2668032 x^{6} + 6828300 x^{5} + 12239667 x^{4} + 15607998 x^{3} + 13676040 x^{2} + 8496738 x + 2906361$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(18 t^{3} + 18 t^{2} + 18\right) x^{2} + \left(18 t^{3} + 9 t + 9\right) x + 18 t^{3} + 9 t^{2} + 18 t + 3$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.4 |
$12$ |
$x^{12} + 72 x^{11} + 1998 x^{10} + 32736 x^{9} + 358668 x^{8} + 1188270 x^{7} + 2200338 x^{6} + 2552472 x^{5} + 2111184 x^{4} + 1374516 x^{3} + 809676 x^{2} + 377622 x + 110889$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(9 t^{3} + 18 t^{2} + 18\right) x^{2} + \left(9 t^{3} + 18 t^{2} + 9 t + 18\right) x + 18 t^{3} + 18 t^{2} + 21$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.6 |
$12$ |
$x^{12} - 90 x^{11} + 3924 x^{10} - 89466 x^{9} + 1161054 x^{8} - 817128 x^{7} + 3238272 x^{6} - 1471608 x^{5} + 3823848 x^{4} - 1189620 x^{3} + 2218104 x^{2} - 383940 x + 490698$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(18 t^{3} + 18 t^{2} + 9 t\right) x^{2} + 9 t^{2} x + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[3, 0]$ |
$[1]$ |
| 3.12.20.7 |
$12$ |
$x^{12} - 108 x^{11} + 4896 x^{10} - 96216 x^{9} + 843858 x^{8} - 299376 x^{7} + 2281014 x^{6} + 1400652 x^{5} + 1282797 x^{4} + 388908 x^{3} + 488430 x^{2} + 251748 x + 110889$ |
$3$ |
$3$ |
$4$ |
$20$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 3/2, 3/2, 5/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(18 t^{3} + 9 t^{2}\right) x^{2} + \left(9 t^{2} + 18 t + 9\right) x + 18 t^{3} + 18 t^{2} + 21$ |
$[3, 0]$ |
$[1]$ |
| 3.12.22.11 |
$12$ |
$x^{12} + 6 x^{9} + 327 x^{6} + 324 x^{4} + 90 x^{3} + 81 x^{2} + 54 x + 18$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 21\right) x^{3} + \left(9 t + 9\right) x + 3 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.15 |
$12$ |
$x^{12} - 42 x^{9} + 18 x^{7} + 876 x^{6} + 756 x^{5} - 54 x^{4} + 630 x^{3} + 513 x^{2} - 54 x + 153$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 21 t x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 12 t + 9$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.16 |
$12$ |
$x^{12} + 24 x^{9} + 129 x^{6} + 108 x^{4} - 216 x^{3} + 324 x^{2} + 432 x + 288$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 15\right) x^{3} + \left(18 t + 18\right) x + 12 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.19 |
$12$ |
$x^{12} + 18 x^{9} - 18 x^{7} + 219 x^{6} + 432 x^{5} + 594 x^{4} + 1098 x^{3} + 1161 x^{2} + 810 x + 450$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(12 t + 21\right) x^{3} + \left(18 t + 18\right) x^{2} + \left(18 t + 9\right) x + 21 t + 18$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.23 |
$12$ |
$x^{12} - 12 x^{9} - 36 x^{8} + 18 x^{7} + 453 x^{6} + 972 x^{5} + 540 x^{4} + 324 x^{3} + 945 x^{2} - 216 x + 288$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(21 t + 15\right) x^{3} + 18 t x^{2} + 9 x + 12 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.24 |
$12$ |
$x^{12} + 12 x^{9} + 36 x^{8} + 336 x^{6} + 216 x^{5} + 324 x^{4} + 612 x^{3} - 432 x^{2} + 585$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 24\right) x^{3} + 18 x^{2} + 21 t + 9$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.42 |
$12$ |
$x^{12} - 18 x^{9} + 18 x^{8} + 18 x^{7} + 516 x^{6} - 162 x^{5} + 297 x^{4} + 1098 x^{3} + 108 x^{2} + 324 x + 450$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(21 t + 12\right) x^{3} + 9 x^{2} + \left(9 t + 18\right) x + 21 t + 18$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.46 |
$12$ |
$x^{12} - 30 x^{9} + 18 x^{7} + 543 x^{6} - 270 x^{4} + 198 x^{3} + 81 x^{2} - 54 x + 18$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 3\right) x^{3} + 9 x + 3 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.5 |
$12$ |
$x^{12} - 18 x^{8} + 36 x^{7} + 66 x^{6} + 108 x^{5} + 162 x^{4} - 288 x^{3} + 108 x^{2} + 540 x + 234$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + 9 t x^{2} + 18 x + 3 t + 18$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.60 |
$12$ |
$x^{12} + 6 x^{9} + 111 x^{6} + 216 x^{4} + 378 x^{3} + 81 x^{2} + 378 x + 882$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(12 t + 15\right) x^{3} + \left(9 t + 9\right) x + 21 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.8 |
$12$ |
$x^{12} + 6 x^{9} - 18 x^{8} + 3 x^{6} - 54 x^{5} + 162 x^{4} - 18 x^{3} + 108 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{3} + 9 t x^{2} + 3 t$ |
$[6, 0]$ |
$[2, 1]$ |
| 3.12.22.9 |
$12$ |
$x^{12} - 30 x^{9} - 36 x^{8} + 36 x^{7} + 507 x^{6} + 1188 x^{5} + 108 x^{4} + 738 x^{3} + 1836 x^{2} - 756 x + 882$ |
$3$ |
$6$ |
$2$ |
$22$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[5/2]$ |
$[3/2, 2, 2, 5/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 3\right) x^{3} + 18 t x^{2} + 18 x + 21 t$ |
$[6, 0]$ |
$[2, 1]$ |
