| 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 |
| 2.4.4.44a1.1 |
$16$ |
$( x^{4} + x + 1 )^{4} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_4 \times D_4$ (as 16T19) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.2 |
$16$ |
$( x^{4} + x + 1 )^{4} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_8:C_2):C_2$ (as 16T16) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.3 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times D_4):C_4$ (as 16T315) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.4 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times D_4):C_4$ (as 16T315) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.5 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3.C_2^3$ (as 16T112) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{4}$ |
$[1,1,2,3]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.6 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$\OD_{16}:C_2^2$ (as 16T99) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{4}$ |
$[1,1,2,3]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.7 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_4 \times D_4$ (as 16T19) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.8 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_8:C_2):C_2$ (as 16T16) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.9 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.10 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.11 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.12 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.13 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.14 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.15 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.16 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.17 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.18 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.19 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.20 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.21 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.22 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.23 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.24 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.25 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.26 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.27 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.28 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.29 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.30 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.31 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.32 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.33 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.34 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.35 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.36 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.37 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.38 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.39 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.40 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.41 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.D_4$ (as 16T208) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.42 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times C_8):D_4$ (as 16T279) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.43 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^5:C_4$ (as 16T261) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.44 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.45 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.D_4$ (as 16T268) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.46 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$\OD_{16}:D_4$ (as 16T278) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.47 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.D_4$ (as 16T317) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.48 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times D_4):C_4$ (as 16T315) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.49 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.D_4$ (as 16T208) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.50 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times C_8):D_4$ (as 16T279) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
