| 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 |
| 2.2.8.32c1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4\wr C_2$ (as 16T42) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4^2:C_4$ (as 16T174) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, \frac{5}{2}]^{4}$ |
$[1,1,1,\frac{3}{2}]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$QD_{16}$ (as 16T12) |
$2$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_{16}$ (as 16T14) |
$2$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{4} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4^2.C_4$ (as 16T139) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, \frac{5}{2}]^{4}$ |
$[1,1,1,\frac{3}{2}]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c1.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4^2.C_4$ (as 16T139) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, \frac{5}{2}]^{4}$ |
$[1,1,1,\frac{3}{2}]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{4} + 4 x^{3} + 4 x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c1.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4\wr C_2$ (as 16T28) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + \left(4 t + 4\right) x^{3} + 4 x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c1.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4^2:C_4$ (as 16T154) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, \frac{5}{2}]^{4}$ |
$[1,1,1,\frac{3}{2}]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c1.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4\wr C_2$ (as 16T28) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{3} + 4 x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c1.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4\wr C_2$ (as 16T42) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_4^2:C_4$ (as 16T174) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, \frac{5}{2}]^{4}$ |
$[1,1,1,\frac{3}{2}]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{3} + 4 x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$QD_{16}$ (as 16T12) |
$2$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{3} + 4 x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c1.13 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_{16}$ (as 16T14) |
$2$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x^{4} + 4 x^{3} + 4 x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + 1$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T684) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T684) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{4} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c2.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^3.C_2\wr C_4$ (as 16T828) |
$8$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{8}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{8}$ |
$[2,2,\frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c2.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^3.C_2\wr C_4$ (as 16T828) |
$8$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{8}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{8}$ |
$[2,2,\frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{4} + 4 t x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c2.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T684) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 t x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c2.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T684) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{4} + 4 t x + 6$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 9, 17]$ |
| 2.2.8.32c2.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^3.C_2\wr C_4$ (as 16T828) |
$8$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{8}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{8}$ |
$[2,2,\frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + \left(4 t + 4\right) x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c2.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^3.C_2\wr C_4$ (as 16T828) |
$8$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{8}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{8}$ |
$[2,2,\frac{5}{2}]^{4}$ |
$[1,1,\frac{3}{2}]^{4}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{4} + \left(4 t + 4\right) x + 4 t + 2$ |
$[9, 6, 6, 0]$ |
$[1, 1]$ |
$z^6 + 1,z + t$ |
$[1, 3, 6, 16]$ |
| 2.2.8.32c3.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 4\right) x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + \left(4 t + 4\right) x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 t x^{3} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c3.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$Q_8^2:C_6$ (as 16T730) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{6}$ |
$[2,2,\frac{5}{2}]^{3}$ |
$[1,1,\frac{3}{2}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 4\right) x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + \left(4 t + 4\right) x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{4} + 4 t x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c4.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{3} + 4 t x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{4} + 4 x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{4} + 4 t x^{3} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c5.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2^8:C_{12}$ (as 16T1754) |
not computed |
not computed |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 t x^{4} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 6, 0]$ |
$[3, 1]$ |
$z^6 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.32c6.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2\wr A_4$ (as 16T427) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{3}$ |
$[1,1]^{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c6.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$(C_2^2\times C_4):A_4$ (as 16T426) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{3}$ |
$[1,1]^{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + \left(4 t + 2\right) x^{4} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c6.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4:(C_2\times A_4)$ (as 16T716) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2,2]^{3}$ |
$[1,1,1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 t x^{3} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c6.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4:(C_2\times A_4)$ (as 16T716) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2,2]^{3}$ |
$[1,1,1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + \left(4 t + 2\right) x^{4} + 4 t x^{3} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c6.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2\wr A_4$ (as 16T427) |
$6$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}]^{6}$ |
$[1,1,1,1,\frac{3}{2}]^{6}$ |
$[2,2]^{3}$ |
$[1,1]^{3}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[3, 1]$ |
$z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 15]$ |
