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Properties

Label 2.1.18.28a
Base 2.1.1.0a1.1
Degree \(18\)
e \(18\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{18} + 2 b_{17} x^{17} + 2 b_{15} x^{15} + 2 b_{13} x^{13} + 2 a_{11} x^{11} + 4 c_{22} x^{4} + 4 b_{21} x^{3} + 4 b_{19} x + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $18$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Artin slopes: $[\frac{20}{9}]$
Swan slopes: $[\frac{11}{9}]$
Means: $\langle\frac{11}{18}\rangle$
Rams: $(11)$
Field count: $64$ (complete)
Ambiguity: $2$
Mass: $32$
Absolute Mass: $32$

Diagrams

Varying

Indices of inseparability: $[11,0]$
Associated inertia: $[6,1]$
Jump Set: $[9,27]$

Galois groups and Hidden Artin slopes

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Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
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Showing 1-50 of 64

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
2.1.18.28a1.1 8 $x^{18} + 2 x^{11} + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.2 8 $x^{18} + 2 x^{11} + 4 x^{4} + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.3 8 $x^{18} + 2 x^{11} + 4 x^{3} + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.4 8 $x^{18} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.5 8 $x^{18} + 2 x^{11} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.6 8 $x^{18} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.7 8 $x^{18} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.8 8 $x^{18} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.9 8 $x^{18} + 2 x^{17} + 2 x^{11} + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.10 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{4} + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.11 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{3} + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.12 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.13 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.14 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.15 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.16 8 $x^{18} + 2 x^{17} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.17 8 $x^{18} + 2 x^{15} + 2 x^{11} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.18 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.19 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{3} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.20 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.21 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.22 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.23 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.24 8 $x^{18} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.25 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.26 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.27 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{3} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.28 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.29 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.30 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.31 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T434) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.32 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^6:C_9:C_6$ (as 18T433) $3456$ $2$ $[\frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.33 16 $x^{18} + 2 x^{13} + 2 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.34 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.35 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{3} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.36 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.37 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.38 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.39 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.40 16 $x^{18} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.41 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.42 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.43 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{3} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.44 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.45 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.46 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.47 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.48 16 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.49 16 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.28a1.50 16 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 4 x^{4} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}, \frac{20}{9}]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},2,\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9},\frac{20}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},1,\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9},\frac{11}{9}]^{6}$ $[11, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
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