| 8.0.418195493.1 |
x8 - x7 + 3x6 - 3x5 + 2x4 - 2x3 + 5x2 + 5x + 1 |
\( 53^{5} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.1997331875.1 |
x8 - x6 - 3x5 - x4 + 4x3 + 4x2 - 2x - 1 |
\( -\,5^{4}\cdot 7^{4}\cdot 11^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.3036027392.1 |
x8 - x7 + 2x6 - 4x5 + 3x4 + 5x3 + 3x2 - 9x + 8 |
\( 2^{9}\cdot 181^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.3157114563.1 |
x8 - 2x7 + x6 + x5 + 7x4 - 14x3 + 7x2 + 7x + 1 |
\( -\,3^{6}\cdot 163^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.4991443829.1 |
x8 - x7 + x6 + 4x5 - x4 - 3x3 + 5x2 - 2x + 1 |
\( 1709^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.7727161833.1 |
x8 - 2x6 - 2x5 + 6x4 + 8x3 + 5x2 + x + 1 |
\( 3^{3}\cdot 659^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.9460870875.1 |
x8 - 2x7 - 2x6 + 10x5 + 7x4 - 11x3 - 11x2 - 2x + 1 |
\( -\,3^{6}\cdot 5^{3}\cdot 47^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.10330523392.1 |
x8 - 2x7 + 7x4 - 14x2 + 8x + 5 |
\( -\,2^{8}\cdot 7^{9} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.10720659157.1 |
x8 - x7 + 2x6 - 5x5 + 6x4 + 2x3 - 2x2 - 5x + 3 |
\( 13^{3}\cdot 47^{4} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.12057493063.2 |
x8 - 3x7 + 7x4 - 7x2 - x - 4 |
\( -\,7^{7}\cdot 11^{4} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.13875904827.1 |
x8 - 2x7 - x6 + 4x5 - 2x4 + 8x3 - 2x2 - 2x - 1 |
\( -\,3^{9}\cdot 89^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.14270199808.1 |
x8 + 4x6 - 8x5 + 6x4 - 8x3 + 2x2 - 4x - 1 |
\( -\,2^{11}\cdot 191^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.14952627621.1 |
x8 - 2x7 - 3x5 + 6x4 + 3x3 - 3x2 + 3 |
\( 3^{6}\cdot 29^{5} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.15748562368.1 |
x8 - 4x7 + 6x6 - 4x5 - 2x4 + 6x3 - 4x2 - 6x + 8 |
\( -\,2^{6}\cdot 7^{5}\cdot 11^{4} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.16209796869.1 |
x8 + 7x6 + 21x4 + 21x2 - 18x + 21 |
\( 3^{9}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.16387080192.5 |
x8 - 4x6 - 8x5 + 32x3 + 16x2 - 1 |
\( -\,2^{16}\cdot 3^{6}\cdot 7^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.18624991792.1 |
x8 - 2x7 + x6 - 3x5 - 6x4 - 7x3 - 6x2 - 8x - 2 |
\( -\,2^{4}\cdot 11^{4}\cdot 43^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.21562200000.1 |
x8 - x7 - 4x5 + 8x3 + 2x2 - 2 |
\( -\,2^{6}\cdot 3^{4}\cdot 5^{5}\cdot 11^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.22105827328.1 |
x8 - 4x7 + 6x6 - 4x5 + 4x4 - 4x3 - 8x + 1 |
\( -\,2^{11}\cdot 13^{3}\cdot 17^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.23328000000.1 |
x8 - 3x7 + 5x6 - 20x5 + 60x4 - 100x3 + 100x2 - 60x + 20 |
\( 2^{11}\cdot 3^{6}\cdot 5^{6} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.24616775429.1 |
x8 - x7 + x6 - 4x4 + 4x2 - x + 1 |
\( 2909^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.29019350017.1 |
x8 - x7 - 4x6 + 3x5 + 5x4 + 2x3 + 4x2 - 3x + 1 |
\( 7^{3}\cdot 439^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.29076046875.1 |
x8 - x7 - 6x6 - 4x5 + 30x4 - x3 - 24x2 - 9x - 1 |
\( -\,3^{3}\cdot 5^{6}\cdot 41^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.29132817533.1 |
x8 - 2x7 + 4x6 - 7x4 + 3x3 + 5x2 - 4x + 1 |
\( 17^{3}\cdot 181^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.31637227888.1 |
x8 - x7 - 7x6 + 7x2 - 27x - 1 |
\( -\,2^{4}\cdot 7^{11} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.32941720000.1 |
x8 - 3x7 + 14x4 - 14x2 - 10x + 2 |
\( -\,2^{6}\cdot 5^{4}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.37797742016.1 |
x8 - x7 + 4x5 - 4x3 - 20x2 - 16x - 20 |
\( -\,2^{6}\cdot 839^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.41135081408.1 |
x8 - 2x7 + 2x4 + 2x3 - 6x2 + 2x + 4 |
\( -\,2^{6}\cdot 863^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.47756222027.1 |
x8 - 2x7 + 2x6 + 3x5 - 5x4 - x3 + 7x2 + x - 2 |
\( -\,17^{4}\cdot 83^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.52437868857.5 |
x8 - 3x7 + 9x6 - 21x5 + 42x4 - 45x3 + 57x2 - 75x + 36 |
\( 3^{6}\cdot 11^{4}\cdot 17^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[6]$
|
| 8.2.53971714048.5 |
x8 - 4x7 + 14x4 - 8x + 4 |
\( -\,2^{16}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.62587167125.1 |
x8 - 2x7 + 8x6 - 13x5 + 22x4 - 27x3 + 22x2 + 7x + 3 |
\( 5^{3}\cdot 7^{5}\cdot 31^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.65477433301.2 |
x8 - 4x7 + 14x6 - 28x5 + 49x4 - 56x3 + 63x2 - 36x + 32 |
\( 7^{7}\cdot 43^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.72313663744.1 |
x8 - x7 + 7x6 + 4x - 4 |
\( -\,2^{8}\cdot 7^{10} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.75622356992.1 |
x8 - x7 + 7x6 - 4x + 4 |
\( 2^{11}\cdot 7^{5}\cdot 13^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.82644187136.1 |
x8 - 3x7 + 7x6 - 14x5 + 28x4 - 14x3 + 56x2 + 26x + 6 |
\( 2^{11}\cdot 7^{9} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.83167327125.1 |
x8 - x7 + 4x6 - 4x5 - 5x4 - x3 + 7x2 + 5x + 1 |
\( 3^{6}\cdot 5^{3}\cdot 97^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.2.86452249968.1 |
x8 - 21x4 + 28x2 - 54x - 63 |
\( -\,2^{4}\cdot 3^{8}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.86452249968.2 |
x8 - 3x7 + 7x6 - 7x2 - 9x - 1 |
\( -\,2^{4}\cdot 3^{8}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.88941805312.1 |
x8 - 2x7 + 2x6 + 6x5 + 7x4 + 6x3 - 8x2 + 2x + 5 |
\( -\,2^{8}\cdot 19^{3}\cdot 37^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.90700411157.1 |
x8 - x7 + 2x6 + 3x5 - 4x3 + 4x2 + 3x + 1 |
\( 4493^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.106025300837.1 |
x8 - 3x7 + x6 + 6x5 - x4 - 2x3 + x2 + 4x + 4 |
\( 4733^{3} \) |
$\PGL(2,7)$ (as 8T43) |
$[3]$
|
| 8.0.109243802493.1 |
x8 - x7 - 7x5 + 28x4 - 42x3 + 28x2 - 7x + 21 |
\( 3^{3}\cdot 7^{7}\cdot 17^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.117786700827.1 |
x8 - x7 - x6 - 5x5 - 7x4 - 5x3 - 4x2 - 4x - 1 |
\( -\,3^{3}\cdot 257^{4} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.128178518272.1 |
x8 - 2x7 - 28x2 + 8x - 16 |
\( -\,2^{8}\cdot 7^{5}\cdot 31^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.128735281503.1 |
x8 - x7 - 5x6 + 7x5 + 2x4 + 7x3 - 7x2 + 4x - 1 |
\( -\,3^{7}\cdot 389^{3} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.131766880000.1 |
x8 - 4x7 + 14x5 + 7x4 - 42x3 + 8x + 31 |
\( -\,2^{8}\cdot 5^{4}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.2.131766880000.2 |
x8 - 2x7 - 7x4 - 4x + 1 |
\( -\,2^{8}\cdot 5^{4}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
$[2]$
|
| 8.2.139968000000.9 |
x8 - 2x7 + x6 - 12x5 + 15x4 - 12x3 + 19x2 - 2x + 19 |
\( -\,2^{12}\cdot 3^{7}\cdot 5^{6} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
| 8.0.145888171821.1 |
x8 - x7 + 7x6 + 7x5 + 35x4 + 28x3 + 28x2 + 11x + 10 |
\( 3^{11}\cdot 7^{7} \) |
$\PGL(2,7)$ (as 8T43) |
Trivial
|
