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Properties

Label 2.1.16.48o
Base 2.1.1.0a1.1
Degree \(16\)
e \(16\)
f \(1\)
c \(48\)

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Defining polynomial

$x^{16} + 4 b_{30} x^{14} + 4 b_{28} x^{12} + 4 a_{26} x^{10} + \left(2 a_{8} + 8 c_{40}\right) x^{8} + 8 b_{39} x^{7} + 8 b_{37} x^{5} + 4 b_{20} x^{4} + 8 b_{35} x^{3} + 8 a_{33} x + 4 c_{16} + 8 c_{32} + 2$

Invariants

Residue field characteristic: $2$
Degree: $16$
Base field: $\Q_{2}$
Ramification index $e$: $16$
Residue field degree $f$: $1$
Discriminant exponent $c$: $48$
Artin slopes: $[2,3,3,\frac{7}{2}]$
Swan slopes: $[1,2,2,\frac{5}{2}]$
Means: $\langle\frac{1}{2},\frac{5}{4},\frac{13}{8},\frac{33}{16}\rangle$
Rams: $(1,3,3,7)$
Field count: $152$ (complete)
Ambiguity: $8$
Mass: $64$
Absolute Mass: $64$

Diagrams

Varying

Indices of inseparability: $[33,26,20,8,0]$ (show 64), $[33,26,24,8,0]$ (show 88)
Associated inertia: $[1,2,1]$ (show 88), $[1,3,1]$ (show 64)
Jump Set: $[1,2,4,8,32]$ (show 76), $[1,2,13,29,45]$ (show 32), $[1,5,10,32,48]$ (show 12), $[1,5,15,31,47]$ (show 20), $[1,5,17,33,49]$ (show 12)

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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 76

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
2.1.16.48o1.45 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.46 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.47 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.48 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x^{7} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.49 4 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x + 6$ $C_2^3.D_4$ (as 16T148) $64$ $2$ $[2, 3, 3, \frac{7}{2}]^{4}$ $[1,2,2,\frac{5}{2}]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.50 4 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 6$ $C_2^3.D_4$ (as 16T148) $64$ $2$ $[2, 3, 3, \frac{7}{2}]^{4}$ $[1,2,2,\frac{5}{2}]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.51 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.52 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.53 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.54 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.55 16 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.56 16 $x^{16} + 4 x^{14} + 4 x^{10} + 10 x^{8} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.57 8 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.58 8 $x^{16} + 4 x^{14} + 4 x^{10} + 10 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.59 4 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{3} + 8 x + 6$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.60 8 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.61 16 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x + 14$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.62 16 $x^{16} + 4 x^{14} + 4 x^{10} + 10 x^{8} + 8 x + 14$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.63 8 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 14$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.64 8 $x^{16} + 4 x^{14} + 4 x^{10} + 10 x^{8} + 8 x^{3} + 8 x + 14$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.65 4 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{3} + 8 x + 14$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.66 8 $x^{16} + 4 x^{14} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 14$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.67 8 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x + 6$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.68 8 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x + 6$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.69 8 $x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 8 x + 6$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.70 4 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 6$ $C_4^2:C_2$ (as 16T30) $32$ $4$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.71 16 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.72 16 $x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{3} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.73 8 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x + 14$ $C_2^4.C_2^3$ (as 16T229) $128$ $2$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.74 8 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x + 14$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.75 8 $x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 8 x + 14$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.76 4 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x + 14$ $C_4^2:C_2$ (as 16T30) $32$ $4$ $[2, 3, 3, \frac{7}{2}]^{2}$ $[1,2,2,\frac{5}{2}]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.77 16 $x^{16} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 14$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.78 16 $x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{3} + 8 x + 14$ $C_2^5.(C_2\times D_4)$ (as 16T833) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.79 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.80 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.81 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.82 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 8 x + 6$ $C_2^5.(C_2\times D_4)$ (as 16T874) $512$ $2$ $[2, 2, 2, 3, 3, 3, \frac{7}{2}]^{4}$ $[1,1,1,2,2,2,\frac{5}{2}]^{4}$ $[2,2,3]^{4}$ $[1,1,2]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.83 4 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{3} + 8 x + 6$ $C_2\wr C_4$ (as 16T166) $64$ $2$ $[2, 3, 3, \frac{7}{2}]^{4}$ $[1,2,2,\frac{5}{2}]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.84 4 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{3} + 8 x + 6$ $C_2\wr C_4$ (as 16T166) $64$ $2$ $[2, 3, 3, \frac{7}{2}]^{4}$ $[1,2,2,\frac{5}{2}]^{4}$ $[\ ]^{4}$ $[\ ]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.85 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.86 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.87 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o1.88 16 $x^{16} + 4 x^{14} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{7} + 8 x^{5} + 8 x^{3} + 8 x + 6$ $C_2^4.D_4$ (as 16T230) $128$ $4$ $[2, 2, 3, 3, \frac{7}{2}]^{4}$ $[1,1,2,2,\frac{5}{2}]^{4}$ $[2]^{4}$ $[1]^{4}$ $[33, 26, 24, 8, 0]$ $[1, 2, 1]$ $z^8 + 1,z^6 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.33 8 $x^{16} + 4 x^{10} + 2 x^{8} + 4 x^{4} + 8 x + 6$ $C_2\wr A_4$ (as 16T425) $192$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[2,2]^{3}$ $[1,1]^{3}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.34 8 $x^{16} + 4 x^{10} + 10 x^{8} + 4 x^{4} + 8 x + 6$ $C_2\wr A_4$ (as 16T425) $192$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{3}$ $[1,1,1,2,2,\frac{5}{2}]^{3}$ $[2,2]^{3}$ $[1,1]^{3}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.35 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x + 6$ $C_2^4:(C_2\times A_4)$ (as 16T723) $384$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$ $[1,1,1,2,2,\frac{5}{2}]^{6}$ $[2,2]^{6}$ $[1,1]^{6}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.36 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x + 6$ $C_2^4:(C_2\times A_4)$ (as 16T723) $384$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$ $[1,1,1,2,2,\frac{5}{2}]^{6}$ $[2,2]^{6}$ $[1,1]^{6}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.37 16 $x^{16} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 4 x^{4} + 8 x + 6$ $C_2^4:(C_2\times A_4)$ (as 16T723) $384$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$ $[1,1,1,2,2,\frac{5}{2}]^{6}$ $[2,2]^{6}$ $[1,1]^{6}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.48o2.38 16 $x^{16} + 4 x^{10} + 10 x^{8} + 8 x^{5} + 4 x^{4} + 8 x + 6$ $C_2^4:(C_2\times A_4)$ (as 16T723) $384$ $2$ $[2, 2, 2, 3, 3, \frac{7}{2}]^{6}$ $[1,1,1,2,2,\frac{5}{2}]^{6}$ $[2,2]^{6}$ $[1,1]^{6}$ $[33, 26, 20, 8, 0]$ $[1, 3, 1]$ $z^8 + 1,z^6 + z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
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