| 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 |
| 2.3.6.18a1.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$C_3\times S_4$ (as 18T30) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + 1)$ |
$[3, 7]$ |
| 2.3.6.18a1.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{2} + 2 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$C_3\times S_4$ (as 18T33) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + 1)$ |
$[3, 7]$ |
| 2.3.6.18a2.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$C_2^4:(C_3\times S_4)$ (as 18T269) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{2} + 2 t^{2} x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.3.6.18a2.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{2} + 2 x ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$C_2^4:(C_3\times S_4)$ (as 18T270) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.3.6.18a3.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$A_4\wr C_2$ (as 18T112) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 7]$ |
| 2.3.6.18a3.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x^{2} ( x^{3} + x + 1 )^{2} + \left(2 x + 2\right) ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$6$ |
$18$ |
$A_4\wr C_2$ (as 18T113) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{2} + \left(2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 7]$ |
| 2.3.6.24a1.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{6}$ |
$[1]_{3}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 6]$ |
| 2.3.6.24a1.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$S_3 \times C_6$ (as 18T6) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{6}$ |
$[1]_{3}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 12]$ |
| 2.3.6.24a1.3 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4^2:C_2^2$ (as 18T175) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a1.4 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4^2:C_2^2$ (as 18T175) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a1.5 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_6\times S_4$ (as 18T61) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a1.6 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_6\times S_4$ (as 18T61) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a1.7 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a1.8 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t)$ |
$[3, 11]$ |
| 2.3.6.24a2.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.3 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x^{2} ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.4 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x^{2} ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.5 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.6 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.7 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.8 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.9 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4\times D_6$ (as 18T60) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]_{3}^{6}$ |
$[1,1,1]_{3}^{6}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.10 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4\times D_6$ (as 18T60) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]_{3}^{6}$ |
$[1,1,1]_{3}^{6}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.11 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4^2:C_2^2$ (as 18T176) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{5} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.12 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4^2:C_2^2$ (as 18T176) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + 2 t^{2} x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.13 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.14 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.15 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{5} + \left(2 t^{2} + 2 t\right) x^{3} + 6$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a2.16 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x + 2\right) ( x^{3} + x + 1 )^{5} + 2 x ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t^{2} x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + (t^2 + t + 1)$ |
$[3, 9]$ |
| 2.3.6.24a3.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T462) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t^{2} + 2\right) x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T463) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t^{2} + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.3 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x^{2} ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T271) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.4 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x^{2} ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T268) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.5 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4\times S_4$ (as 18T114) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.6 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 x ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$A_4\times S_4$ (as 18T115) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t + 2\right) x^{5} + \left(2 t^{2} + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.7 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T271) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t + 2\right) x^{3} + 4 t^{2} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.8 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T268) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.9 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T462) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + \left(2 t + 2\right) x^{3} + 4 t^{2} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.10 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T463) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.11 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T271) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t^{2} x^{5} + \left(2 t^{2} + 2\right) x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.12 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(S_3\times A_4)$ (as 18T268) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.13 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T462) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(2 t^{2} + 2 t + 2\right) x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.14 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$C_2^4:(A_4\times S_4)$ (as 18T463) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2 t\right) x^{5} + \left(2 t^{2} + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.15 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$S_3\times A_4$ (as 18T32) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{3} + 4 t^{2} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.24a3.16 |
$18$ |
$( x^{3} + x + 1 )^{6} + \left(2 x^{2} + 2 x + 2\right) ( x^{3} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{3} + x + 1 )^{3} + 4 x^{2} + 2$ |
$2$ |
$3$ |
$6$ |
$24$ |
$S_3\times A_4$ (as 18T31) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + \left(2 t^{2} + 2\right) x^{3} + 2$ |
$[3, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.3.6.30a1.1 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 2$ |
$2$ |
$3$ |
$6$ |
$30$ |
$C_6\times S_4$ (as 18T61) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,\frac{8}{3}]^{2}$ |
$[1,\frac{5}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 9]$ |
| 2.3.6.30a1.2 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{4} + 2$ |
$2$ |
$3$ |
$6$ |
$30$ |
$C_6\times S_4$ (as 18T61) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,\frac{8}{3}]^{2}$ |
$[1,\frac{5}{3}]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{4} + 2$ |
$[5, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 9]$ |
| 2.3.6.30a1.3 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$30$ |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,\frac{8}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,\frac{5}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + \left(4 t^{2} + 4 t\right) x^{3} + 2$ |
$[5, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 9]$ |
| 2.3.6.30a1.4 |
$18$ |
$( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{4} + 4 x ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$6$ |
$30$ |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,\frac{8}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,\frac{5}{3}]^{2}$ |
$2$ |
$t^{3} + t + 1$ |
$x^{6} + 2 x^{5} + 4 x^{4} + 4 t^{2} x^{3} + 2$ |
$[5, 0]$ |
$[2, 1]$ |
$z^4 + z^2 + 1,z + t^2$ |
$[3, 9]$ |
