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Properties

Label 2.1.18.35a
Base 2.1.1.0a1.1
Degree \(18\)
e \(18\)
f \(1\)
c \(35\)

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Defining polynomial

$x^{18} + 4 b_{35} x^{17} + 4 b_{33} x^{15} + 4 b_{31} x^{13} + 4 b_{29} x^{11} + 4 b_{27} x^{9} + 4 b_{25} x^{7} + 4 b_{23} x^{5} + 4 b_{21} x^{3} + 4 b_{19} x + 8 c_{36} + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $18$
Residue field degree $f$: $1$
Discriminant exponent $c$: $35$
Artin slopes: $[3]$
Swan slopes: $[2]$
Means: $\langle1\rangle$
Rams: $(18)$
Field count: $1024$ (complete)
Ambiguity: $2$
Mass: $512$
Absolute Mass: $512$

Diagrams

Varying

Indices of inseparability: $[18,0]$
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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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
2.1.18.35a1.1 4 $x^{18} + 2$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[3]_{9}^{6}$ $[2]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.2 4 $x^{18} + 10$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[3]_{9}^{6}$ $[2]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.3 4 $x^{18} + 4 x^{17} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.4 4 $x^{18} + 4 x^{17} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.5 4 $x^{18} + 4 x^{15} + 2$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.6 4 $x^{18} + 4 x^{15} + 10$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.7 4 $x^{18} + 4 x^{17} + 4 x^{15} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.8 4 $x^{18} + 4 x^{17} + 4 x^{15} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.9 8 $x^{18} + 4 x^{13} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.10 8 $x^{18} + 4 x^{13} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.11 8 $x^{18} + 4 x^{17} + 4 x^{13} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.12 8 $x^{18} + 4 x^{17} + 4 x^{13} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.13 8 $x^{18} + 4 x^{15} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.14 8 $x^{18} + 4 x^{15} + 4 x^{13} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.15 8 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.16 8 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.17 16 $x^{18} + 4 x^{11} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.18 16 $x^{18} + 4 x^{11} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.19 16 $x^{18} + 4 x^{17} + 4 x^{11} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.20 16 $x^{18} + 4 x^{17} + 4 x^{11} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.21 16 $x^{18} + 4 x^{15} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.22 16 $x^{18} + 4 x^{15} + 4 x^{11} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.23 16 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.24 16 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{11} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.25 16 $x^{18} + 4 x^{13} + 4 x^{11} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.26 16 $x^{18} + 4 x^{13} + 4 x^{11} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.27 16 $x^{18} + 4 x^{17} + 4 x^{13} + 4 x^{11} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.28 16 $x^{18} + 4 x^{17} + 4 x^{13} + 4 x^{11} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.29 16 $x^{18} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.30 16 $x^{18} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.31 16 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.32 16 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.33 4 $x^{18} + 4 x^{9} + 2$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[3]_{9}^{6}$ $[2]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.34 4 $x^{18} + 4 x^{9} + 10$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[3]_{9}^{6}$ $[2]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.35 4 $x^{18} + 4 x^{17} + 4 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.36 4 $x^{18} + 4 x^{17} + 4 x^{9} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.37 4 $x^{18} + 4 x^{15} + 4 x^{9} + 2$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.38 4 $x^{18} + 4 x^{15} + 4 x^{9} + 10$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.39 4 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.40 4 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{9} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 3]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},2]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.41 8 $x^{18} + 4 x^{13} + 4 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.42 8 $x^{18} + 4 x^{13} + 4 x^{9} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.43 8 $x^{18} + 4 x^{17} + 4 x^{13} + 4 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.44 8 $x^{18} + 4 x^{17} + 4 x^{13} + 4 x^{9} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.45 8 $x^{18} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.46 8 $x^{18} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.47 8 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.48 8 $x^{18} + 4 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 10$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 3]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},2]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.49 16 $x^{18} + 4 x^{11} + 4 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.35a1.50 16 $x^{18} + 4 x^{11} + 4 x^{9} + 10$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 3]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},2]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[18, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
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