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Properties

Label 2.1.18.34a
Base 2.1.1.0a1.1
Degree \(18\)
e \(18\)
f \(1\)
c \(34\)

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Defining polynomial

$x^{18} + 2 a_{17} x^{17} + 4 c_{34} x^{16} + 4 b_{33} x^{15} + 4 b_{31} x^{13} + 4 b_{29} x^{11} + 4 b_{27} x^{9} + 4 b_{25} x^{7} + 4 b_{23} x^{5} + 4 b_{21} x^{3} + 4 b_{19} x + 2$

Invariants

Residue field characteristic: $2$
Degree: $18$
Base field: $\Q_{2}$
Ramification index $e$: $18$
Residue field degree $f$: $1$
Discriminant exponent $c$: $34$
Artin slopes: $[\frac{26}{9}]$
Swan slopes: $[\frac{17}{9}]$
Means: $\langle\frac{17}{18}\rangle$
Rams: $(17)$
Field count: $512$ (complete)
Ambiguity: $2$
Mass: $256$
Absolute Mass: $256$

Diagrams

Varying

Indices of inseparability: $[17,0]$
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 512

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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
2.1.18.34a1.1 128 $x^{18} + 2 x^{17} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.2 128 $x^{18} + 2 x^{17} + 4 x^{16} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.3 128 $x^{18} + 2 x^{17} + 4 x^{15} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.4 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.5 128 $x^{18} + 2 x^{17} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.6 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.7 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.8 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.9 128 $x^{18} + 2 x^{17} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.10 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.11 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.12 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.13 128 $x^{18} + 2 x^{17} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.14 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.15 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.16 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.17 128 $x^{18} + 2 x^{17} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.18 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.19 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.20 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.21 128 $x^{18} + 2 x^{17} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.22 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.23 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.24 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.25 128 $x^{18} + 2 x^{17} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.26 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.27 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.28 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.29 128 $x^{18} + 2 x^{17} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.30 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.31 128 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.32 128 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_9.C_6$ (as 18T656) $27648$ $2$ $[2, \frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[2,\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[1,\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.33 64 $x^{18} + 2 x^{17} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.34 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.35 64 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.36 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.37 64 $x^{18} + 2 x^{17} + 4 x^{13} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.38 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.39 64 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.40 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.41 64 $x^{18} + 2 x^{17} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.42 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.43 64 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.44 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.45 64 $x^{18} + 2 x^{17} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.46 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.47 64 $x^{18} + 2 x^{17} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.48 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{15} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.49 64 $x^{18} + 2 x^{17} + 4 x^{9} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T588) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
2.1.18.34a1.50 64 $x^{18} + 2 x^{17} + 4 x^{16} + 4 x^{9} + 4 x^{7} + 2$ $C_2^2:A_4^2.S_4$ (as 18T592) $13824$ $2$ $[\frac{8}{3}, \frac{8}{3}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}, \frac{26}{9}]_{9}^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]_{9}^{6}$ $[\frac{8}{3},\frac{8}{3},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9},\frac{26}{9}]^{6}$ $[\frac{5}{3},\frac{5}{3},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9},\frac{17}{9}]^{6}$ $[17, 0]$ $[6, 1]$ $z^{16} + z^{14} + 1,z + 1$ $[9, 27]$
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