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Properties

Label 3.1.12.21a
Base 3.1.1.0a1.1
Degree \(12\)
e \(12\)
f \(1\)
c \(21\)

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Defining polynomial

$x^{12} + 3 b_{11} x^{11} + 3 a_{10} x^{10} + 9 c_{15} x^{3} + 9 b_{14} x^{2} + 9 b_{13} x + 3 d_{0}$

Invariants

Residue field characteristic: $3$
Degree: $12$
Base field: $\Q_{3}$
Ramification index $e$: $12$
Residue field degree $f$: $1$
Discriminant exponent $c$: $21$
Artin slopes: $[\frac{9}{4}]$
Swan slopes: $[\frac{5}{4}]$
Means: $\langle\frac{5}{6}\rangle$
Rams: $(5)$
Field count: $114$ (complete)
Ambiguity: $6$
Mass: $54$
Absolute Mass: $54$

Diagrams

Varying

Indices of inseparability: $[10,0]$
Associated inertia: $[2,1]$ (show 84), $[2,2]$ (show 30)
Jump Set: undefined (show 57), $[2,14]$ (show 57)

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 57

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
3.1.12.21a1.1 6 $x^{12} + 6 x^{10} + 3$ $\SOPlus(4,2)$ (as 12T36) $72$ $2$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.2 6 $x^{12} + 6 x^{10} + 9 x^{2} + 3$ $\SOPlus(4,2)$ (as 12T36) $72$ $2$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.3 6 $x^{12} + 6 x^{10} + 18 x^{2} + 3$ $\SOPlus(4,2)$ (as 12T36) $72$ $2$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.4 6 $x^{12} + 6 x^{10} + 9 x + 3$ $S_3^2:S_3$ (as 12T120) $216$ $1$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.5 6 $x^{12} + 6 x^{10} + 9 x^{2} + 9 x + 3$ $S_3^2:S_3$ (as 12T120) $216$ $1$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.6 6 $x^{12} + 6 x^{10} + 18 x^{2} + 9 x + 3$ $S_3^2:S_3$ (as 12T120) $216$ $1$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.7 12 $x^{12} + 3 x^{11} + 6 x^{10} + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.8 12 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.9 12 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.10 12 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.11 12 $x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.12 12 $x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ $C_3^3:D_{12}$ (as 12T169) $648$ $1$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.13 6 $x^{12} + 6 x^{11} + 6 x^{10} + 9 x + 3$ $C_3^2:D_{12}$ (as 12T118) $216$ $1$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.14 6 $x^{12} + 6 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ $C_3^2:D_{12}$ (as 12T118) $216$ $1$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a1.15 6 $x^{12} + 6 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ $C_3^2:D_{12}$ (as 12T118) $216$ $1$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 2]$ $z^9 + z^6 + 1,z^2 + 1$ $[2, 14]$
3.1.12.21a2.1 6 $x^{12} + 3 x^{10} + 3$ $\SOPlus(4,2)$ (as 12T35) $72$ $6$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.2 6 $x^{12} + 3 x^{10} + 9 x^{3} + 3$ $S_3^2:C_6$ (as 12T121) $216$ $3$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.3 6 $x^{12} + 3 x^{10} + 9 x^{2} + 3$ $\SOPlus(4,2)$ (as 12T35) $72$ $6$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.4 6 $x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ $S_3^2:C_6$ (as 12T121) $216$ $3$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.5 6 $x^{12} + 3 x^{10} + 18 x^{2} + 3$ $\SOPlus(4,2)$ (as 12T35) $72$ $6$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{9}{4}]^{2}$ $[\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.6 6 $x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ $S_3^2:C_6$ (as 12T121) $216$ $3$ $[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{9}{4}]^{6}$ $[\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.7 6 $x^{12} + 3 x^{10} + 9 x + 3$ $S_3^2:S_3$ (as 12T116) $216$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.8 12 $x^{12} + 3 x^{10} + 9 x^{3} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.9 12 $x^{12} + 3 x^{10} + 18 x^{3} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.10 6 $x^{12} + 3 x^{10} + 9 x^{2} + 9 x + 3$ $S_3^2:S_3$ (as 12T116) $216$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.11 12 $x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.12 12 $x^{12} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.13 6 $x^{12} + 3 x^{10} + 18 x^{2} + 9 x + 3$ $S_3^2:S_3$ (as 12T116) $216$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},\frac{9}{4}]^{2}$ $[\frac{1}{2},\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.14 12 $x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.15 12 $x^{12} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ $[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ $[\frac{3}{2},\frac{9}{4}]^{6}$ $[\frac{1}{2},\frac{5}{4}]^{6}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.16 36 $x^{12} + 3 x^{11} + 3 x^{10} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.17 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.18 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.19 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.20 36 $x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.21 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.22 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.23 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.24 36 $x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{3} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.25 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.26 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.27 36 $x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.28 36 $x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.29 36 $x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.30 36 $x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.31 36 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.32 36 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.33 36 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ $C_3\wr D_4$ (as 12T167) $648$ $3$ $[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[\frac{3}{2},2,\frac{9}{4}]^{2}$ $[\frac{1}{2},1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.34 18 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x + 3$ $S_3^2:C_6$ (as 12T121) $216$ $3$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
3.1.12.21a2.35 18 $x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{3} + 9 x + 3$ $S_3^2:C_6$ (as 12T121) $216$ $3$ $[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ $[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ $[2,\frac{9}{4}]^{2}$ $[1,\frac{5}{4}]^{2}$ $[10, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z^2 + 2$ $[2, 14]$
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