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Properties

Label 2.1.14.27a
Base 2.1.1.0a1.1
Degree \(14\)
e \(14\)
f \(1\)
c \(27\)

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Defining polynomial

$x^{14} + 4 b_{27} x^{13} + 4 b_{25} x^{11} + 4 b_{23} x^{9} + 4 b_{21} x^{7} + 4 b_{19} x^{5} + 4 b_{17} x^{3} + 4 b_{15} x + 8 c_{28} + 2$

Invariants

Residue field characteristic: $2$
Degree: $14$
Base field: $\Q_{2}$
Ramification index $e$: $14$
Residue field degree $f$: $1$
Discriminant exponent $c$: $27$
Artin slopes: $[3]$
Swan slopes: $[2]$
Means: $\langle1\rangle$
Rams: $(14)$
Field count: $256$ (complete)
Ambiguity: $2$
Mass: $128$
Absolute Mass: $128$

Diagrams

Varying

Indices of inseparability: $[14,0]$
Associated inertia: $[3,1]$
Jump Set: $[7,21]$

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 256

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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
2.1.14.27a1.1 4 $x^{14} + 2$ $(C_7:C_3) \times C_2$ (as 14T5) $42$ $2$ $[3]_{7}^{3}$ $[2]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.2 4 $x^{14} + 10$ $(C_7:C_3) \times C_2$ (as 14T5) $42$ $2$ $[3]_{7}^{3}$ $[2]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.3 4 $x^{14} + 4 x^{13} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.4 4 $x^{14} + 4 x^{13} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.5 4 $x^{14} + 4 x^{11} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.6 4 $x^{14} + 4 x^{11} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.7 4 $x^{14} + 4 x^{13} + 4 x^{11} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.8 4 $x^{14} + 4 x^{13} + 4 x^{11} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.9 8 $x^{14} + 4 x^{9} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.10 8 $x^{14} + 4 x^{9} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.11 8 $x^{14} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.12 8 $x^{14} + 4 x^{13} + 4 x^{9} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.13 8 $x^{14} + 4 x^{11} + 4 x^{9} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.14 8 $x^{14} + 4 x^{11} + 4 x^{9} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.15 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.16 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.17 4 $x^{14} + 4 x^{7} + 2$ $(C_7:C_3) \times C_2$ (as 14T5) $42$ $2$ $[3]_{7}^{3}$ $[2]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.18 4 $x^{14} + 4 x^{7} + 10$ $(C_7:C_3) \times C_2$ (as 14T5) $42$ $2$ $[3]_{7}^{3}$ $[2]_{7}^{3}$ $[\ ]^{3}$ $[\ ]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.19 4 $x^{14} + 4 x^{13} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.20 4 $x^{14} + 4 x^{13} + 4 x^{7} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.21 4 $x^{14} + 4 x^{11} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.22 4 $x^{14} + 4 x^{11} + 4 x^{7} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.23 4 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.24 4 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{7} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{10}{7},\frac{10}{7},\frac{10}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{3}{7},\frac{3}{7},\frac{3}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.25 8 $x^{14} + 4 x^{9} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.26 8 $x^{14} + 4 x^{9} + 4 x^{7} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.27 8 $x^{14} + 4 x^{13} + 4 x^{9} + 4 x^{7} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.28 8 $x^{14} + 4 x^{13} + 4 x^{9} + 4 x^{7} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.29 8 $x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.30 8 $x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.31 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.32 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 4 x^{7} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{8}{7}, \frac{8}{7}, \frac{8}{7}, \frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 3]_{7}^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7},2]_{7}^{3}$ $[\frac{8}{7},\frac{8}{7},\frac{8}{7},\frac{12}{7},\frac{12}{7},\frac{12}{7}]^{3}$ $[\frac{1}{7},\frac{1}{7},\frac{1}{7},\frac{5}{7},\frac{5}{7},\frac{5}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.33 8 $x^{14} + 4 x^{5} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.34 8 $x^{14} + 4 x^{5} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.35 8 $x^{14} + 4 x^{13} + 4 x^{5} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.36 8 $x^{14} + 4 x^{13} + 4 x^{5} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.37 8 $x^{14} + 4 x^{11} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.38 8 $x^{14} + 4 x^{11} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.39 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.40 8 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.41 16 $x^{14} + 4 x^{9} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.42 16 $x^{14} + 4 x^{9} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.43 16 $x^{14} + 4 x^{13} + 4 x^{9} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.44 16 $x^{14} + 4 x^{13} + 4 x^{9} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.45 16 $x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.46 16 $x^{14} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.47 16 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.48 16 $x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 4 x^{5} + 10$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.49 8 $x^{14} + 4 x^{7} + 4 x^{5} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.27a1.50 8 $x^{14} + 4 x^{7} + 4 x^{5} + 10$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}, 3]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7},2]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[14, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
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