↑

Properties

Label 2.3.6.33a
Base 2.1.1.0a1.1
Degree \(18\)
e \(6\)
f \(3\)
c \(33\)

Related objects

Downloads

Learn more

Defining polynomial over unramified subextension

$x^{6} + 4 b_{11} x^{5} + 4 b_{9} x^{3} + 4 b_{7} x + 8 c_{12} + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $6$
Residue field degree $f$: $3$
Discriminant exponent $c$: $33$
Artin slopes: $[3]$
Swan slopes: $[2]$
Means: $\langle1\rangle$
Rams: $(6)$
Field count: $352$ (complete)
Ambiguity: $6$
Mass: $512$
Absolute Mass: $512/3$

Diagrams

Varying

Indices of inseparability: $[6,0]$
Associated inertia: $[2,1]$
Jump Set: $[3,9]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
Sort order Select

Showing 1-50 of 352

Next   displayed columns for results
Label Packet size Polynomial Galois group Galois degree $\#\Aut(K/\Q_p)$ Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.3.6.33a1.1 4 $( x^{3} + x + 1 )^{6} + 2$ $S_3 \times C_6$ (as 18T6) $36$ $6$ $[3]_{3}^{6}$ $[2]_{3}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.2 4 $( x^{3} + x + 1 )^{6} + 10$ $S_3 \times C_6$ (as 18T6) $36$ $6$ $[3]_{3}^{6}$ $[2]_{3}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.3 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 2$ $A_4^2:C_2^2$ (as 18T175) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.4 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 10$ $A_4^2:C_2^2$ (as 18T175) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.5 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 2$ $C_6\times S_4$ (as 18T61) $144$ $6$ $[\frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.6 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 10$ $C_6\times S_4$ (as 18T61) $144$ $6$ $[\frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.7 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 2$ $C_2^4:(C_6\times S_4)$ (as 18T367) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.8 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 10$ $C_2^4:(C_6\times S_4)$ (as 18T367) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.9 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $A_4\times D_6$ (as 18T60) $144$ $2$ $[2, 2, 3]_{3}^{6}$ $[1,1,2]_{3}^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.10 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $A_4\times D_6$ (as 18T60) $144$ $2$ $[2, 2, 3]_{3}^{6}$ $[1,1,2]_{3}^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.11 12 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.12 12 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.13 12 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.14 12 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.15 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.16 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.17 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $A_4^2:C_2^2$ (as 18T176) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.18 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $A_4^2:C_2^2$ (as 18T176) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.19 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.20 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.21 12 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.22 12 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.23 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.24 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 x ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.25 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{3} + 2$ $S_3 \times C_6$ (as 18T6) $36$ $6$ $[3]_{3}^{6}$ $[2]_{3}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.26 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{3} + 10$ $S_3 \times C_6$ (as 18T6) $36$ $6$ $[3]_{3}^{6}$ $[2]_{3}^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.27 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 2$ $A_4^2:C_2^2$ (as 18T175) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.28 4 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 10$ $A_4^2:C_2^2$ (as 18T175) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.29 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 2$ $C_6\times S_4$ (as 18T61) $144$ $6$ $[\frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.30 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 10$ $C_6\times S_4$ (as 18T61) $144$ $6$ $[\frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.31 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(C_6\times S_4)$ (as 18T367) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.32 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + 4 ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(C_6\times S_4)$ (as 18T367) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.33 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $A_4\times D_6$ (as 18T60) $144$ $2$ $[2, 2, 3]_{3}^{6}$ $[1,1,2]_{3}^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.34 4 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $A_4\times D_6$ (as 18T60) $144$ $2$ $[2, 2, 3]_{3}^{6}$ $[1,1,2]_{3}^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.35 12 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.36 12 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.37 12 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.38 12 $( x^{3} + x + 1 )^{6} + 4 x ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.39 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.40 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^4:(A_4\times D_6)$ (as 18T366) $2304$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.41 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $A_4^2:C_2^2$ (as 18T176) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.42 4 $( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $A_4^2:C_2^2$ (as 18T176) $576$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.43 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.44 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.45 12 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.46 12 $( x^{3} + x + 1 )^{6} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.47 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.48 12 $( x^{3} + x + 1 )^{6} + \left(4 x^{2} + 4 x + 4\right) ( x^{3} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{3} + x + 1 )^{3} + 10$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1,2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2,2]^{2}$ $[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.49 48 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{3} + 4 x^{2} ( x^{3} + x + 1 ) + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
2.3.6.33a1.50 48 $( x^{3} + x + 1 )^{6} + 4 x^{2} ( x^{3} + x + 1 )^{5} + 4 x^{2} ( x^{3} + x + 1 )^{3} + 4 x^{2} ( x^{3} + x + 1 ) + 2$ $C_2^5.(A_4\times S_4)$ (as 18T544) $9216$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, 3]_{3}^{6}$ $[\frac{1}{3},\frac{1}{3},1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3},2]_{3}^{6}$ $[\frac{4}{3},\frac{4}{3},2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{2}$ $[\frac{1}{3},\frac{1}{3},1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{2}$ $[6, 0]$ $[2, 1]$ $z^4 + z^2 + 1,z + t$ $[3, 9]$
Next   displayed columns for results