↑

Properties

Label 2.1.14.22a
Base 2.1.1.0a1.1
Degree \(14\)
e \(14\)
f \(1\)
c \(22\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{14} + 2 b_{13} x^{13} + 2 b_{11} x^{11} + 2 a_{9} x^{9} + 4 c_{18} x^{4} + 4 b_{17} x^{3} + 4 b_{15} x + 2$

Invariants

Residue field characteristic: $2$
Degree: $14$
Base field: $\Q_{2}$
Ramification index $e$: $14$
Residue field degree $f$: $1$
Discriminant exponent $c$: $22$
Artin slopes: $[\frac{16}{7}]$
Swan slopes: $[\frac{9}{7}]$
Means: $\langle\frac{9}{14}\rangle$
Rams: $(9)$
Field count: $32$ (complete)
Ambiguity: $2$
Mass: $16$
Absolute Mass: $16$

Diagrams

Varying

Indices of inseparability: $[9,0]$
Associated inertia: $[3,1]$
Jump Set: $[7,21]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set Fields per packet
Sort order Select

Showing all 32

  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
2.1.14.22a1.1 2 $x^{14} + 2 x^{9} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.2 2 $x^{14} + 2 x^{9} + 4 x^{4} + 2$ $F_8:C_3$ (as 14T11) $168$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.3 2 $x^{14} + 2 x^{9} + 4 x^{3} + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.4 2 $x^{14} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$ $F_8:C_3$ (as 14T11) $168$ $2$ $[\frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.5 2 $x^{14} + 2 x^{9} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.6 2 $x^{14} + 2 x^{9} + 4 x^{4} + 4 x + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.7 2 $x^{14} + 2 x^{9} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.8 2 $x^{14} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.9 4 $x^{14} + 2 x^{13} + 2 x^{9} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.10 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{4} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.11 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.12 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.13 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.14 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{4} + 4 x + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.15 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{6}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{6}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{6}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.16 4 $x^{14} + 2 x^{13} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2^3:F_8:C_3$ (as 14T35) $1344$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.17 8 $x^{14} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.18 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.19 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.20 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.21 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.22 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.23 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.24 8 $x^{14} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{12}{7}, \frac{12}{7}, \frac{12}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{12}{7},\frac{12}{7},\frac{12}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{5}{7},\frac{5}{7},\frac{5}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.25 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.26 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.27 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.28 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2$ $C_2\wr C_7:C_3$ (as 14T44) $2688$ $2$ $[\frac{10}{7}, \frac{10}{7}, \frac{10}{7}, 2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[\frac{10}{7},\frac{10}{7},\frac{10}{7},2,\frac{16}{7},\frac{16}{7}]^{3}$ $[\frac{3}{7},\frac{3}{7},\frac{3}{7},1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.29 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[2,\frac{16}{7},\frac{16}{7}]^{3}$ $[1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.30 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[2,\frac{16}{7},\frac{16}{7}]^{3}$ $[1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.31 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[2,\frac{16}{7},\frac{16}{7}]^{3}$ $[1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
2.1.14.22a1.32 4 $x^{14} + 2 x^{13} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $F_8:C_6$ (as 14T18) $336$ $2$ $[2, \frac{16}{7}, \frac{16}{7}, \frac{16}{7}]_{7}^{3}$ $[1,\frac{9}{7},\frac{9}{7},\frac{9}{7}]_{7}^{3}$ $[2,\frac{16}{7},\frac{16}{7}]^{3}$ $[1,\frac{9}{7},\frac{9}{7}]^{3}$ $[9, 0]$ $[3, 1]$ $z^{12} + z^{10} + z^8 + z^6 + z^4 + z^2 + 1,z + 1$ $[7, 21]$
  displayed columns for results