| 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 |
| 2.2.8.56a5.793 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.794 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.795 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.796 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.797 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.798 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.799 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.800 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.841 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.842 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.843 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.844 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.845 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.846 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.847 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.848 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.873 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.874 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.875 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.876 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.877 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.878 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.879 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.880 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.889 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.890 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.891 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.892 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.893 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.894 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.895 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.896 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.897 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.898 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.899 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.900 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.901 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.902 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.903 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.904 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.937 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.938 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.939 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.940 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.941 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.942 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.943 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.944 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.945 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.946 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[\frac{15}{4},\frac{15}{4},2,2,\frac{5}{2},\frac{7}{2}]$ |
$[\frac{11}{4},\frac{11}{4},1,1,\frac{3}{2},\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
