Properties

Label 2.1.14.24a
Base 2.1.1.0a1.1
Degree \(14\)
e \(14\)
f \(1\)
c \(24\)

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Defining polynomial

$x^{14} + 2 b_{13} x^{13} + 2 a_{11} x^{11} + 4 c_{22} x^{8} + 4 b_{21} x^{7} + 4 b_{19} x^{5} + 4 b_{17} x^{3} + 4 b_{15} x + 2$

Invariants

Residue field characteristic: $2$
Degree: $14$
Base field: $\Q_{2}$
Ramification index $e$: $14$
Residue field degree $f$: $1$
Discriminant exponent $c$: $24$
Artin slopes: $[\frac{18}{7}]$
Swan slopes: $[\frac{11}{7}]$
Means: $\langle\frac{11}{14}\rangle$
Rams: $(11)$
Field count: $64$ (complete)
Ambiguity: $2$
Mass: $32$
Absolute Mass: $32$

Diagrams

Varying

Indices of inseparability: $[11,0]$
Associated inertia: $[3,1]$
Jump Set: $[7,21]$

Galois groups and Hidden Artin slopes

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Fields


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
2.1.14.24a1.1 $x^{14} + 2 x^{11} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.2 $x^{14} + 2 x^{11} + 4 x^{8} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.3 $x^{14} + 2 x^{11} + 4 x^{7} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.4 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.5 $x^{14} + 2 x^{11} + 4 x^{5} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.6 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.7 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.8 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.9 $x^{14} + 2 x^{11} + 4 x^{3} + 2$ $F_8:C_3$ (as 14T11) $168$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.10 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{3} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.11 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{3} + 2$ $F_8:C_3$ (as 14T11) $168$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.12 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.13 $x^{14} + 2 x^{11} + 4 x^{5} + 4 x^{3} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.14 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.15 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.16 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.17 $x^{14} + 2 x^{11} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.18 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.19 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.20 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.21 $x^{14} + 2 x^{11} + 4 x^{5} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.22 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.23 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.24 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.25 $x^{14} + 2 x^{11} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.26 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.27 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.28 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.29 $x^{14} + 2 x^{11} + 4 x^{5} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.30 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.31 $x^{14} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.32 $x^{14} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.33 $x^{14} + 2 x^{13} + 2 x^{11} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.34 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.35 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.36 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[2,\frac{18}{7},\frac{18}{7}]^{3}$ $[1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.37 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.38 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.39 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.40 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.41 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.42 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.43 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{7} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.44 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.45 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.46 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.47 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.48 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.49 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x + 2$ $F_8:C_3$ (as 14T11) $168$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{3}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{3}$ $[\frac{18}{7},\frac{18}{7}]^{3}$ $[\frac{11}{7},\frac{11}{7}]^{3}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.24a1.50 $x^{14} + 2 x^{13} + 2 x^{11} + 4 x^{8} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{18}{7}, \frac{18}{7}, \frac{18}{7}]_{7}^{6}$ $[\frac{11}{7},\frac{11}{7},\frac{11}{7}]_{7}^{6}$ $[\frac{18}{7},\frac{18}{7}]^{6}$ $[\frac{11}{7},\frac{11}{7}]^{6}$ $[11, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
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