| 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 |
| 2.2.8.56a1.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.13 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.14 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.15 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.16 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.17 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.18 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.19 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.20 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.33 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_2\times C_4^2):C_4$ (as 16T291) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.35 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.36 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.43 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.44 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.47 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.48 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.49 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.50 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.59 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.60 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.61 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.62 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.63 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.64 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.65 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.66 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.67 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.68 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.69 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.70 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.71 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.72 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.73 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.74 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8):C_4$ (as 16T294) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.75 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.76 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.77 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.78 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.79 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.80 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.81 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.82 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}.D_4$ (as 16T215) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 16 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.105 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 24 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.106 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 24 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$\OD_{16}:D_4$ (as 16T251) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 8 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
