| 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 |
| 2.2.8.16a1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$16$ |
$F_8:C_6$ (as 16T712) |
$6$ |
$7$ |
$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$ |
$[\frac{1}{7},\frac{1}{7},\frac{1}{7}]$ |
$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]_{7}^{6}$ |
$[\frac{1}{7},\frac{1}{7},\frac{1}{7}]_{7}^{6}$ |
$[\ ]^{3}_{7}$ |
$[\ ]^{3}_{7}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x + 2$ |
$[1, 1, 1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2, 4, 9]$ |
| 2.2.8.16a2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$16$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}]$ |
$[\frac{1}{7},\frac{1}{7},\frac{1}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x + 2$ |
$[1, 1, 1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 2, 4, 9]$ |
| 2.2.8.20a1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$F_8:C_6$ (as 16T712) |
$6$ |
$7$ |
$[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$ |
$[\frac{3}{7},\frac{3}{7},\frac{3}{7}]$ |
$[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]_{7}^{6}$ |
$[\frac{3}{7},\frac{3}{7},\frac{3}{7}]_{7}^{6}$ |
$[\ ]^{3}_{7}$ |
$[\ ]^{3}_{7}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{3} + 2$ |
$[3, 3, 3, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2, 4, 11]$ |
| 2.2.8.20a2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}]$ |
$[\frac{3}{7},\frac{3}{7},\frac{3}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{3} + 2$ |
$[3, 3, 3, 0]$ |
$[1]$ |
$z + t$ |
$[1, 2, 4, 11]$ |
| 2.2.8.20b1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$\GL(2,3)$ (as 16T66) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b1.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2.S_4$ (as 16T65) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 11]$ |
| 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) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, \frac{3}{2}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2}]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{3} + 2 x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b3.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 2 x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b3.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, \frac{3}{2}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b4.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b4.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 2 t x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b5.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + (t + 1)$ |
$[1, 2, 5, 11]$ |
| 2.2.8.20b5.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{4} + 2 x ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$20$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, \frac{3}{2}]$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + \left(2 t + 2\right) x^{3} + 2 t x^{2} + 2$ |
$[3, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + (t + 1)$ |
$[1, 2, 5, 11]$ |
| 2.2.8.24a1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$F_8:C_6$ (as 16T712) |
$6$ |
$7$ |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]_{7}^{6}$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]_{7}^{6}$ |
$[\ ]^{3}_{7}$ |
$[\ ]^{3}_{7}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2$ |
$[5, 5, 5, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3, 6, 13]$ |
| 2.2.8.24a1.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 t x^{4} + 2$ |
$[5, 5, 4, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3, 6, 13]$ |
| 2.2.8.24a1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$F_8:C_6$ (as 16T712) |
$6$ |
$7$ |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]_{7}^{6}$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]_{7}^{6}$ |
$[\ ]^{3}_{7}$ |
$[\ ]^{3}_{7}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{4} + 2$ |
$[5, 5, 4, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2, 4, 13]$ |
| 2.2.8.24a2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2$ |
$[5, 5, 5, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3, 6, 13]$ |
| 2.2.8.24a2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 t x^{4} + 2$ |
$[5, 5, 4, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3, 6, 13]$ |
| 2.2.8.24a2.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 x^{4} + 2$ |
$[5, 5, 4, 0]$ |
$[1]$ |
$z + t$ |
$[1, 2, 4, 13]$ |
| 2.2.8.24a2.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^3:F_8:C_6$ (as 16T1501) |
not computed |
not computed |
$[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}]$ |
$[\frac{5}{7},\frac{5}{7},\frac{5}{7}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{5} + 2 t x^{4} + 2$ |
$[5, 5, 4, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3, 6, 13]$ |
| 2.2.8.24b1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\GL(2,3)$ (as 16T66) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.2.8.24b1.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2.S_4$ (as 16T65) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 x^{2} + 4 t + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.2.8.24b1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^4.\GL(2,3)$ (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) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{3}{2}, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},\frac{3}{2}]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{2}]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 x^{5} + 2 x^{2} + 4 t + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 15]$ |
| 2.2.8.24b1.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2\times S_4$ (as 16T61) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 10]$ |
| 2.2.8.24b1.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$A_4:C_4$ (as 16T62) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 4 t + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 5, 16]$ |
| 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) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 t x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\GL(2,3):C_2$ (as 16T192) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[2]_{3}$ |
$[1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 t x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\GL(2,3):C_2$ (as 16T192) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[2]_{3}$ |
$[1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 t x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[2]_{3}$ |
$[1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 t x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b2.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\GL(2,\mathbb{Z}/4)$ (as 16T193) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[2]_{3}$ |
$[1]_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 t x^{5} + 2 x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 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) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{4}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$A_4^2:D_4$ (as 16T1286) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$A_4^2:D_4$ (as 16T1286) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b3.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + 1$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$\SL(2,3)\wr C_2$ (as 16T1291) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 t x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 x ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{7} + 2 t x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 t x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$24$ |
$C_2^7.A_4\wr C_2$ (as 16T1825) |
not computed |
not computed |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{7} + 2 t x^{5} + 2 t x^{2} + 2$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
| 2.2.8.24b4.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$24$ |
$A_4^2:D_4$ (as 16T1286) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}, 2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{3}_{3}$ |
$[\frac{1}{3},\frac{1}{3},1]^{3}_{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{7} + 2 t x^{5} + 2 t x^{2} + 6$ |
$[5, 2, 2, 0]$ |
$[1, 1]$ |
$z^2 + t,t z + t$ |
$[1, 2, 5, 13]$ |
