| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.2.8.20b2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, \frac{3}{2}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2}]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, \frac{3}{2}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2}]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 11]$ |
| 2.2.8.24b1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.2.8.24b1.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 x^{5} + 2 x^{2} + 4 t + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.2.8.24b2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 t x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 t x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{3} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{4} + 4 t x^{3} + 2 x^{2} + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{2} + 4 t x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{4} + 2 x^{2} + 4 t x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{4} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.17 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{3} + 2 x^{2} + 4 x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.28b1.18 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$28$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{3}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, \frac{5}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},\frac{3}{2}]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 4 t x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 2$ |
$[7, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.17 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.18 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},2]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.55 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.56 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.59 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.60 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.63 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.64 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.69 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b1.70 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2, \frac{7}{3}, \frac{7}{3}, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2},1,\frac{4}{3},\frac{4}{3},2]_{3}^{2}$ |
$[\frac{3}{2},2,\frac{7}{3},\frac{7}{3}]_{3}$ |
$[\frac{1}{2},1,\frac{4}{3},\frac{4}{3}]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 x + 8 t + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(4 t + 4\right) x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(4 t + 4\right) x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + \left(4 t + 4\right) x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + \left(4 t + 4\right) x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.15 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.16 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.19 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.20 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.21 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.22 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{5} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.27 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.28 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.29 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.30 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{5}{3},\frac{5}{3},2,2]_{3}^{4}$ |
$[\frac{8}{3},\frac{8}{3},3]^{2}_{3}$ |
$[\frac{5}{3},\frac{5}{3},2]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.97 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2,2]_{3}^{2}$ |
$[2,\frac{8}{3},\frac{8}{3},3]_{3}$ |
$[1,\frac{5}{3},\frac{5}{3},2]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 4 t x^{3} + 2 x^{2} + 4 t x + 2$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.32b2.98 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.\GL(2,3)$ (as 16T1069) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 3]$ |
$[\frac{1}{3},\frac{1}{3},2]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}, 3, 3]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3},2,2]_{3}^{2}$ |
$[2,\frac{8}{3},\frac{8}{3},3]_{3}$ |
$[1,\frac{5}{3},\frac{5}{3},2]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 4 t x^{5} + 4 t x^{3} + 2 x^{2} + 4 t x + 10$ |
$[9, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
