| 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 |
| 2.2.8.56a1.39 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.40 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.41 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.42 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.53 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.54 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.55 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.56 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.85 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.86 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.87 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.88 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.91 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.92 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.93 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.94 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.95 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.96 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.97 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.98 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.99 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.100 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.101 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.102 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.161 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.162 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.163 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.164 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.167 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.168 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.169 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.170 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.731 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.732 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 4\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.733 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.734 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 4\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.735 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.736 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.737 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.738 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.741 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 4\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.742 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.743 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 4\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.744 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2}]^{2}$ |
$[1,1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.747 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.748 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.749 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.750 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.795 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.796 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.(C_4\times D_4)$ (as 16T884) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,2,3,4]^{2}$ |
$[1,1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
