| 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 |
| 2.2.8.56a2.305 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.306 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.307 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.308 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.309 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.310 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.311 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.312 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.313 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.314 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.315 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.316 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.317 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.318 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.319 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.320 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.321 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.322 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.323 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.324 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.325 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.326 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.327 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.328 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.329 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.330 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.331 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.332 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.333 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.334 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.335 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.336 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.337 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.338 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.339 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.340 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.341 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.342 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.343 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.344 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.345 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.346 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.347 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.348 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.349 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.350 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.351 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.352 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.353 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 16\right) x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.354 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1281) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2},\frac{9}{2}]$ |
$[\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 8 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
