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Properties

Label 2.1.16.42k
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(42\)

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Defining polynomial

$x^{16} + 4 b_{31} x^{15} + 4 b_{29} x^{13} + 2 a_{12} x^{12} + 4 a_{27} x^{11} + \left(2 b_{8} + 4 c_{24}\right) x^{8} + 4 b_{22} x^{6} + 8 c_{36} x^{4} + 8 b_{35} x^{3} + 4 a_{18} x^{2} + 8 b_{33} x + 4 c_{16} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $42$
Artin slopes: $[2,2,\frac{5}{2},\frac{13}{4}]$
Swan slopes: $[1,1,\frac{3}{2},\frac{9}{4}]$
Means: $\langle\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}\rangle$
Rams: $(1,1,3,9)$
Field count: $160$ (complete)
Ambiguity: $8$
Mass: $64$
Absolute Mass: $64$

Diagrams

Varying

Indices of inseparability: $[27,18,12,8,0]$ (show 80), $[27,18,12,12,0]$ (show 80)
Associated inertia: $[2,1,1]$ (show 80), $[3,1,1]$ (show 80)
Jump Set: $[1,2,7,15,31]$ (show 80), $[1,3,6,12,32]$ (show 40), $[1,3,9,25,41]$ (show 40)

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

Fields

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

Showing 1-50 of 80

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
2.1.16.42k2.1 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.2 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.3 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.4 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.5 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.6 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{3} + 4 x^{2} + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.7 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.8 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.9 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.10 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.11 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.12 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.13 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.14 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.15 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.16 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.17 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.18 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.19 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.20 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.21 $x^{16} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.22 $x^{16} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.23 $x^{16} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.24 $x^{16} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.25 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.26 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{3} + 4 x^{2} + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.27 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.28 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.29 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.30 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.31 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.32 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.33 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.34 $x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.35 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.36 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.37 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.38 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.39 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.40 $x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 6 x^{8} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.41 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.42 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.43 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.44 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$ $C_4\wr A_4$ (as 16T1517) $3072$ $4$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.45 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.46 $x^{16} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 2$ $C_4^3.(C_2\times A_4)$ (as 16T1302) $1536$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.47 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.48 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ not computed not computed not computed not computed $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.49 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
2.1.16.42k2.50 $x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 2 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$ $C_4^4:(C_2\times A_4)$ (as 16T1657) $6144$ $2$ $[2, 2, 2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{6}$ $[2,2,2,2,3,3]^{6}$ $[1,1,1,1,2,2]^{6}$ $[27, 18, 12, 8, 0]$ $[3, 1, 1]$ $z^{12} + z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 7, 15, 31]$
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