| 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 |
| 2.2.8.56a4.1553 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1554 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1555 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1556 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1557 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1558 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1559 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1560 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1569 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1570 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1571 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1572 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1573 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1574 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1575 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1576 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1673 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1674 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1675 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1676 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1677 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1678 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1679 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1680 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1681 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1682 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1683 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1684 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1685 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1686 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1687 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1688 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1689 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1690 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1691 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1692 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1693 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1694 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1695 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1696 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1705 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1706 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1707 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1708 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1709 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1710 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1711 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a4.1712 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 12 ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^6.(C_4\times D_4)$ (as 16T1375) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]^{2}$ |
$[1,1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 16\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
