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Properties

Label 2.1.16.40c
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(40\)

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Defining polynomial

$x^{16} + 4 b_{31} x^{15} + 2 a_{14} x^{14} + 4 b_{29} x^{13} + 2 b_{12} x^{12} + 4 b_{27} x^{11} + 4 a_{25} x^{9} + 2 b_{8} x^{8} + 8 c_{36} x^{4} + 8 b_{35} x^{3} + 8 b_{33} x + 4 c_{16} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $40$
Artin slopes: $[2,2,2,\frac{13}{4}]$
Swan slopes: $[1,1,1,\frac{9}{4}]$
Means: $\langle\frac{1}{2},\frac{3}{4},\frac{7}{8},\frac{25}{16}\rangle$
Rams: $(1,1,1,11)$
Field count: $256$ (complete)
Ambiguity: $4$
Mass: $128$
Absolute Mass: $128$

Diagrams

Varying

Indices of inseparability: $[25,14,12,8,0]$ (show 64), $[25,14,12,12,0]$ (show 64), $[25,14,14,8,0]$ (show 64), $[25,14,14,14,0]$ (show 64)
Associated inertia: $[3,1]$ (show 64), $[4,1]$ (show 64), $[7,1]$ (show 128)
Jump Set: $[1,2,4,15,31]$ (show 64), $[1,2,7,14,32]$ (show 32), $[1,2,7,23,39]$ (show 32), $[1,3,6,15,31]$ (show 64), $[1,3,7,14,32]$ (show 32), $[1,3,7,23,39]$ (show 32)

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
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Showing 1-50 of 256

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
2.1.16.40c1.1 $x^{16} + 2 x^{14} + 4 x^{9} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.2 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.3 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{3} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.4 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.5 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.6 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.7 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{3} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.8 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.9 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.10 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.11 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.12 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.13 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.14 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{3} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.15 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.16 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.17 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.18 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{3} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.19 $x^{16} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.20 $x^{16} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.21 $x^{16} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.22 $x^{16} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.23 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.24 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{11} + 4 x^{9} + 8 x^{3} + 8 x + 2$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.25 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.26 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.27 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{3} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.28 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 2$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.29 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.30 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.31 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{3} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.32 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{11} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 2$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 23, 39]$
2.1.16.40c1.33 $x^{16} + 2 x^{14} + 4 x^{9} + 6$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.34 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 6$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.35 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{3} + 6$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.36 $x^{16} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 6$ $(D_4\times C_2^3):A_4$ (as 16T1037) $768$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[3,3,3]^{6}$ $[2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.37 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 6$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.38 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 6$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.39 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{3} + 6$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.40 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 6$ $C_2^4:(C_2\times A_4)$ (as 16T716) $384$ $2$ $[2, 2, 2, 3, 3, 3, \frac{13}{4}]^{3}$ $[1,1,1,2,2,2,\frac{9}{4}]^{3}$ $[3,3,3]^{3}$ $[2,2,2]^{3}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.41 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ not computed not computed not computed not computed $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.42 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ not computed not computed not computed not computed $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.43 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{3} + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ not computed not computed not computed not computed $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.44 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.45 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{3} + 8 x + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.46 $x^{16} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 8 x^{3} + 8 x + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.47 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ not computed not computed not computed not computed $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.48 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ not computed not computed not computed not computed $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.49 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
2.1.16.40c1.50 $x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 4 x^{9} + 8 x^{4} + 8 x + 6$ $C_2\wr C_2^3:C_3$ (as 16T1658) $6144$ $2$ $[2, 2, 2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{6}$ $[1,1,1,1,1,1,2,2,2,\frac{9}{4}]^{6}$ $[2,2,2,3,3,3]^{6}$ $[1,1,1,2,2,2]^{6}$ $[25, 14, 14, 14, 0]$ $[3, 1]$ $z^{14} + 1,z + 1$ $[1, 3, 7, 14, 32]$
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