| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.8.20.1 |
$8$ |
$x^{8} + 8 x^{7} + 36 x^{6} + 80 x^{5} + 104 x^{4} - 32 x^{3} - 8 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 12\right) x^{2} + 12 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.10 |
$8$ |
$x^{8} + 8 x^{7} + 40 x^{6} + 112 x^{5} + 204 x^{4} + 176 x^{3} + 16 x^{2} - 32 x + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$C_2^3: C_4$ (as 8T20) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.100 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 14$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_4\wr C_2$ (as 8T17) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 14$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.20.101 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_4\wr C_2$ (as 8T17) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{2} + 6$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.20.102 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_4\wr C_2$ (as 8T17) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 6$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.20.103 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_4\wr C_2$ (as 8T17) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{2} + 8 x + 2$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.20.104 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_4\wr C_2$ (as 8T17) |
$2$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$ |
$[13, 6, 6, 0]$ |
$[1, 2]$ |
| 2.8.20.105 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.106 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 4 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.107 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.108 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.109 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 4 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.11 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} - 48 x^{5} + 152 x^{4} + 32 x^{3} + 168 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$C_2^3: C_4$ (as 8T20) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 12 t x^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.110 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.111 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 2 x^{4} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.112 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 12 x^{2} + 10$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 12 x^{2} + 10$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.113 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.114 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 4 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.115 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 12 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 12 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.116 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.117 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.118 |
$8$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.119 |
$8$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 4 x^{7} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.12 |
$8$ |
$x^{8} + 8 x^{7} + 32 x^{6} + 72 x^{5} + 92 x^{4} + 48 x^{3} + 32 x^{2} + 80 x + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$C_2^3: C_4$ (as 8T20) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 8 x^{2} + \left(8 t + 8\right) x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.120 |
$8$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$2$ |
$8$ |
$1$ |
$20$ |
$C_2\wr A_4$ (as 8T38) |
$3$ |
$1$ |
$[2, 2, 7/2]$ |
$[2, 2, 2, 3, 3, 7/2]^{3}$ |
$t + 1$ |
$x^{8} + 2 x^{6} + 4 x^{5} + 14 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[1, 3]$ |
| 2.8.20.13 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{6} + 32 x^{5} + 76 x^{4} + 16 x^{3} + 104 x^{2} - 32 x + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.14 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{6} + 16 x^{5} + 116 x^{4} + 16 x^{3} + 152 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(12 t + 8\right) x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.15 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} - 16 x^{5} + 36 x^{4} + 80 x^{3} - 40 x^{2} + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 4 t x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.16 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} - 16 x^{5} + 28 x^{4} + 48 x^{3} - 24 x^{2} + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 4 t x^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.17 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{6} + 32 x^{5} + 204 x^{4} + 144 x^{3} + 120 x^{2} + 224 x + 196$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(12 t + 8\right) x^{2} + 8 x + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.18 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 48 x^{5} + 68 x^{4} + 80 x^{3} + 168 x^{2} + 148$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 8\right) x^{2} + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.19 |
$8$ |
$x^{8} + 8 x^{7} + 12 x^{6} - 16 x^{5} + 20 x^{4} + 16 x^{3} + 40 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 4 t x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.2 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 68 x^{4} + 80 x^{3} + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t + 4\right) x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.20 |
$8$ |
$x^{8} + 8 x^{7} + 20 x^{6} + 16 x^{5} + 44 x^{4} + 112 x^{3} + 56 x^{2} + 196$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$4$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 3, 7/2]^{4}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 4\right) x^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.21 |
$8$ |
$x^{8} + 4 x^{7} + 40 x^{6} + 40 x^{5} + 196 x^{4} - 56 x^{3} + 304 x^{2} - 80 x + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 12 x^{2} + 8 t x + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.22 |
$8$ |
$x^{8} + 4 x^{7} + 12 x^{6} + 8 x^{5} + 60 x^{4} + 88 x^{3} + 40 x^{2} - 48 x + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 t x^{2} + 8 t x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.23 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 116 x^{4} + 56 x^{3} + 152 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.24 |
$8$ |
$x^{8} - 4 x^{7} + 20 x^{6} + 32 x^{5} - 4 x^{4} + 8 x^{3} + 88 x^{2} + 96 x + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.25 |
$8$ |
$x^{8} - 4 x^{7} + 12 x^{6} + 24 x^{5} + 100 x^{4} + 24 x^{3} + 24 x^{2} - 80 x + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t x^{2} + 8 t x + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.26 |
$8$ |
$x^{8} - 4 x^{7} + 32 x^{6} + 32 x^{5} + 100 x^{4} + 88 x^{3} + 224 x^{2} + 160 x + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t + 12\right) x^{2} + 8 x + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.27 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 120 x^{4} + 88 x^{3} + 232 x^{2} + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.28 |
$8$ |
$x^{8} - 4 x^{7} + 12 x^{6} + 96 x^{5} + 84 x^{4} + 8 x^{3} + 200 x^{2} + 32 x + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(12 t + 4\right) x^{2} + 8 x + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.29 |
$8$ |
$x^{8} - 4 x^{7} + 20 x^{6} + 16 x^{5} + 20 x^{4} + 40 x^{3} + 56 x^{2} + 52$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.3 |
$8$ |
$x^{8} + 8 x^{7} + 28 x^{6} + 64 x^{5} + 216 x^{4} + 128 x^{3} + 328 x^{2} + 64 x + 124$ |
$2$ |
$4$ |
$2$ |
$20$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(12 t + 12\right) x^{2} + 8 x + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.30 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 80 x^{5} + 124 x^{4} + 24 x^{3} + 24 x^{2} + 36$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 8\right) x^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.31 |
$8$ |
$x^{8} + 4 x^{7} + 24 x^{6} + 16 x^{5} + 36 x^{4} + 40 x^{3} + 80 x^{2} + 100$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.32 |
$8$ |
$x^{8} + 4 x^{7} + 20 x^{6} + 24 x^{5} + 60 x^{4} + 104 x^{3} + 136 x^{2} + 48 x + 84$ |
$2$ |
$4$ |
$2$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 8 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.33 |
$8$ |
$x^{8} - 4 x^{7} + 24 x^{6} + 32 x^{5} + 92 x^{4} - 56 x^{3} + 112 x^{2} + 196$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t + 8\right) x^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.34 |
$8$ |
$x^{8} + 4 x^{7} + 24 x^{6} + 16 x^{5} + 28 x^{4} + 72 x^{3} + 48 x^{2} + 84$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 x^{2} + 8 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.8.20.35 |
$8$ |
$x^{8} + 4 x^{7} + 28 x^{6} + 96 x^{5} + 152 x^{4} + 40 x^{3} + 120 x^{2} + 28$ |
$2$ |
$4$ |
$2$ |
$20$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$2$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t + 12\right) x^{2} + 4 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
