2.8.0.1 |
x8 + x4 + x3 + x + 1 |
$2$ |
$1$ |
$8$ |
$0$ |
$C_8$ (as 8T1) |
$ [\ ]^{8}$ |
2.8.8.1 |
x8 + 28x4 + 144 |
$2$ |
$2$ |
$4$ |
$8$ |
$C_4\times C_2$ (as 8T2) |
$ [2]^{4}$ |
2.8.8.10 |
x8 + 2x6 + 8x3 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 2]^{4}$ |
2.8.8.11 |
x8 + 20x2 + 4 |
$2$ |
$4$ |
$2$ |
$8$ |
$S_4$ (as 8T14) |
$ [4/3, 4/3]_{3}^{2}$ |
2.8.8.12 |
x8 + 2x5 + 2x4 + 4 |
$2$ |
$4$ |
$2$ |
$8$ |
$A_4\wr C_2$ (as 8T42) |
$ [4/3, 4/3, 4/3, 4/3]_{3}^{6}$ |
2.8.8.13 |
x8 + 2x + 2 |
$2$ |
$8$ |
$1$ |
$8$ |
$C_2^3:(C_7: C_3)$ (as 8T36) |
$ [8/7, 8/7, 8/7]_{7}^{3}$ |
2.8.8.2 |
x8 + 2x7 + 8x2 + 48 |
$2$ |
$2$ |
$4$ |
$8$ |
$C_2^2:C_4$ (as 8T10) |
$ [2, 2]^{4}$ |
2.8.8.3 |
x8 + 2x7 + 2x6 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$C_2^3: C_4$ (as 8T20) |
$ [2, 2, 2]^{4}$ |
2.8.8.4 |
x8 + 2x7 + 2x6 + 8x3 + 48 |
$2$ |
$2$ |
$4$ |
$8$ |
$C_8$ (as 8T1) |
$ [2]^{4}$ |
2.8.8.5 |
x8 + 2x7 + 8x2 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$C_8:C_2$ (as 8T7) |
$ [2, 2]^{4}$ |
2.8.8.6 |
x8 + 2x7 + 2x6 + 16x2 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$(C_8:C_2):C_2$ (as 8T16) |
$ [2, 2, 2]^{4}$ |
2.8.8.7 |
x8 + 2x6 + 4x5 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 2]^{4}$ |
2.8.8.8 |
x8 + 4x5 + 8x2 + 48 |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 2]^{4}$ |
2.8.8.9 |
x8 + 6x6 + 4x5 + 16 |
$2$ |
$2$ |
$4$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 2]^{4}$ |
2.8.10.1 |
x8 + 2x3 + 2 |
$2$ |
$8$ |
$1$ |
$10$ |
$C_2^3:(C_7: C_3)$ (as 8T36) |
$ [10/7, 10/7, 10/7]_{7}^{3}$ |
2.8.10.2 |
x8 + 20x2 + 20 |
$2$ |
$8$ |
$1$ |
$10$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$ [4/3, 4/3, 3/2]_{3}^{2}$ |
2.8.10.3 |
x8 + 4x2 + 20 |
$2$ |
$8$ |
$1$ |
$10$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$ [4/3, 4/3, 3/2]_{3}^{2}$ |
2.8.12.1 |
x8 + 6x6 + 8x5 + 16 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$ [3]^{4}$ |
2.8.12.10 |
x8 + 2x6 + 112 |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 3]^{4}$ |
2.8.12.11 |
x8 + 6x6 + 48 |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 3]^{4}$ |
2.8.12.12 |
x8 + 2x6 + 48 |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 3]^{4}$ |
2.8.12.13 |
x8 + 12x4 + 16 |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$ [2, 2]^{2}$ |
2.8.12.14 |
x8 + 12x4 + 144 |
$2$ |
$4$ |
$2$ |
$12$ |
$D_4$ (as 8T4) |
$ [2, 2]^{2}$ |
2.8.12.15 |
x8 + 2x7 + 2x4 + 12 |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^2:C_4$ (as 8T10) |
$ [2, 2]^{4}$ |
2.8.12.16 |
x8 + 24x2 + 4 |
$2$ |
$4$ |
$2$ |
$12$ |
$A_4\times C_2$ (as 8T13) |
$ [2, 2]^{6}$ |
2.8.12.17 |
x8 + 2x7 + 2x6 + 2x4 + 4 |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^4:C_6$ (as 8T33) |
$ [2, 2, 2, 2]^{6}$ |
2.8.12.18 |
x8 + 8x7 + 48 |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^4:C_6$ (as 8T33) |
$ [2, 2, 2, 2]^{6}$ |
2.8.12.19 |
x8 + 12x4 + 80 |
$2$ |
$4$ |
$2$ |
$12$ |
$(C_8:C_2):C_2$ (as 8T16) |
$ [2, 2, 2]^{4}$ |
2.8.12.2 |
x8 + 2x6 + 8x4 + 16 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$ [3]^{4}$ |
2.8.12.20 |
x8 + 8x6 + 12x4 + 80 |
$2$ |
$4$ |
$2$ |
$12$ |
$C_2^3: C_4$ (as 8T21) |
$ [2, 2, 2]^{4}$ |
2.8.12.21 |
x8 + 12x6 + 12x4 + 80 |
$2$ |
$4$ |
$2$ |
$12$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$ [2, 2, 2, 2]^{4}$ |
2.8.12.22 |
x8 + 4x7 + 16x3 + 48 |
$2$ |
$4$ |
$2$ |
$12$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$ [2, 2, 2, 2]^{4}$ |
2.8.12.23 |
x8 + 8x5 + 4x4 + 48 |
$2$ |
$4$ |
$2$ |
$12$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$ [2, 2, 2, 2]^{4}$ |
2.8.12.24 |
x8 + 4x6 + 28x4 + 80 |
$2$ |
$4$ |
$2$ |
$12$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$ [2, 2, 2, 2]^{4}$ |
2.8.12.25 |
x8 + 28x2 + 4 |
$2$ |
$8$ |
$1$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$ [4/3, 4/3, 2]_{3}^{2}$ |
2.8.12.26 |
x8 + 12x2 + 4 |
$2$ |
$8$ |
$1$ |
$12$ |
$S_4\times C_2$ (as 8T24) |
$ [4/3, 4/3, 2]_{3}^{2}$ |
2.8.12.27 |
x8 + 4x5 + 4 |
$2$ |
$8$ |
$1$ |
$12$ |
$C_2^3:(C_7: C_3)$ (as 8T36) |
$ [12/7, 12/7, 12/7]_{7}^{3}$ |
2.8.12.28 |
x8 + 2x5 + 2 |
$2$ |
$8$ |
$1$ |
$12$ |
$C_2^3:(C_7: C_3)$ (as 8T36) |
$ [12/7, 12/7, 12/7]_{7}^{3}$ |
2.8.12.29 |
x8 + 28x2 + 20 |
$2$ |
$8$ |
$1$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$ [4/3, 4/3, 2]_{3}^{2}$ |
2.8.12.3 |
x8 + 2x6 + 16x2 + 16 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_2^2:C_4$ (as 8T10) |
$ [2, 3]^{4}$ |
2.8.12.30 |
x8 + 12x2 + 20 |
$2$ |
$8$ |
$1$ |
$12$ |
$\textrm{GL(2,3)}$ (as 8T23) |
$ [4/3, 4/3, 2]_{3}^{2}$ |
2.8.12.4 |
x8 + 2x6 + 16 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_2^3: C_4$ (as 8T20) |
$ [2, 2, 3]^{4}$ |
2.8.12.5 |
x8 + 6x6 + 8x5 + 80 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_8$ (as 8T1) |
$ [3]^{4}$ |
2.8.12.6 |
x8 + 2x6 + 8x4 + 80 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_8$ (as 8T1) |
$ [3]^{4}$ |
2.8.12.7 |
x8 + 4x6 + 8x2 + 80 |
$2$ |
$2$ |
$4$ |
$12$ |
$C_8:C_2$ (as 8T7) |
$ [2, 3]^{4}$ |
2.8.12.8 |
x8 + 2x6 + 80 |
$2$ |
$2$ |
$4$ |
$12$ |
$(C_8:C_2):C_2$ (as 8T16) |
$ [2, 2, 3]^{4}$ |
2.8.12.9 |
x8 + 6x6 + 112 |
$2$ |
$2$ |
$4$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$ [2, 2, 2, 3]^{4}$ |
2.8.14.1 |
x8 + 2x7 + 6 |
$2$ |
$8$ |
$1$ |
$14$ |
$A_4\times C_2$ (as 8T13) |
$ [2, 2, 2]^{3}$ |
2.8.14.10 |
x8 + 4x2 + 28 |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |
2.8.14.11 |
x8 + 20x2 + 12 |
$2$ |
$8$ |
$1$ |
$14$ |
$C_2 \wr S_4$ (as 8T44) |
$ [4/3, 4/3, 2, 7/3, 7/3, 5/2]_{3}^{2}$ |