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Properties

Label 2.1.18.26a
Base 2.1.1.0a1.1
Degree \(18\)
e \(18\)
f \(1\)
c \(26\)

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Defining polynomial

$x^{18} + 2 b_{17} x^{17} + 2 b_{15} x^{15} + 2 b_{13} x^{13} + 2 b_{11} x^{11} + 2 a_{9} x^{9} + 4 c_{18} + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $18$
Residue field degree $f$: $1$
Discriminant exponent $c$: $26$
Artin slopes: $[2]$
Swan slopes: $[1]$
Means: $\langle\frac{1}{2}\rangle$
Rams: $(9)$
Field count: $32$ (complete)
Ambiguity: $2$
Mass: $16$
Absolute Mass: $16$

Diagrams

Varying

Indices of inseparability: $[9,0]$
Associated inertia: $[6,1]$
Jump Set: $[9,18]$ (show 1), $[9,29]$ (show 16), $[9,31]$ (show 8), $[9,33]$ (show 4), $[9,35]$ (show 2), $[9,36]$ (show 1)

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 all 32

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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
2.1.18.26a1.1 2 $x^{18} + 2 x^{9} + 2$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[2]_{9}^{6}$ $[1]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 18]$
2.1.18.26a1.2 2 $x^{18} + 2 x^{9} + 6$ $C_{18}:C_6$ (as 18T45) $108$ $2$ $[2]_{9}^{6}$ $[1]_{9}^{6}$ $[\ ]^{6}$ $[\ ]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 36]$
2.1.18.26a1.3 2 $x^{18} + 2 x^{17} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 2]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},1]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 35]$
2.1.18.26a1.4 2 $x^{18} + 2 x^{17} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, 2]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},1]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 35]$
2.1.18.26a1.5 2 $x^{18} + 2 x^{15} + 2 x^{9} + 2$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 33]$
2.1.18.26a1.6 2 $x^{18} + 2 x^{15} + 2 x^{9} + 6$ $C_6^2.D_6$ (as 18T147) $432$ $2$ $[\frac{4}{3}, \frac{4}{3}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{3},\frac{1}{3}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 33]$
2.1.18.26a1.7 2 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 2]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},1]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 33]$
2.1.18.26a1.8 2 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{4}{3}, \frac{4}{3}, 2]_{9}^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3},1]_{9}^{6}$ $[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{4}{3},\frac{4}{3}]^{6}$ $[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{3},\frac{1}{3}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 33]$
2.1.18.26a1.9 4 $x^{18} + 2 x^{13} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.10 4 $x^{18} + 2 x^{13} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.11 4 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.12 4 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.13 4 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.14 4 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.15 4 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{13} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.16 4 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{13} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 31]$
2.1.18.26a1.17 8 $x^{18} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.18 8 $x^{18} + 2 x^{11} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.19 8 $x^{18} + 2 x^{17} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.20 8 $x^{18} + 2 x^{17} + 2 x^{11} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.21 8 $x^{18} + 2 x^{15} + 2 x^{11} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.22 8 $x^{18} + 2 x^{15} + 2 x^{11} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.23 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.24 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{11} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.25 8 $x^{18} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.26 8 $x^{18} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.27 8 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.28 8 $x^{18} + 2 x^{17} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 6$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[\frac{4}{3}, \frac{4}{3}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{4}{3},\frac{4}{3},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{1}{3},\frac{1}{3},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.29 8 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.30 8 $x^{18} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.31 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
2.1.18.26a1.32 8 $x^{18} + 2 x^{17} + 2 x^{15} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 6$ $C_2^6:C_{18}:C_6$ (as 18T512) $6912$ $2$ $[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, 2]_{9}^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},1]_{9}^{6}$ $[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}$ $[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}$ $[9, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 29]$
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