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Group invariants
| Abstract group: | $C_2^5:(C_4\times S_4)$ |
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| Order: | $3072=2^{10} \cdot 3$ |
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| Cyclic: | no |
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| Abelian: | no |
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| Solvable: | yes |
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| Nilpotency class: | not nilpotent |
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Group action invariants
| Degree $n$: | $24$ |
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| Transitive number $t$: | $5391$ |
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| Parity: | $-1$ |
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| Primitive: | no |
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| $\card{\Aut(F/K)}$: | $2$ |
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| Generators: | $(1,14,2,13)(3,15)(4,16)(5,19,6,20)(7,17)(8,18)(9,22)(10,21)(11,23,12,24)$, $(1,18,9,15,6,23,2,17,10,16,5,24)(3,20,12,13,7,22,4,19,11,14,8,21)$, $(1,3)(2,4)(5,12,6,11)(7,10,8,9)(13,15,14,16)(17,22,18,21)(19,24,20,23)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_4$ x 4, $C_2^2$ x 7 $6$: $S_3$ $8$: $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$ $12$: $D_{6}$ x 3 $16$: $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $C_4\times C_2^2$ $24$: $S_4$, $S_3 \times C_2^2$, $S_3 \times C_4$ x 2 $32$: $C_2^3 : C_4 $ x 2, $C_2 \times (C_2^2:C_4)$ $48$: $S_4\times C_2$ x 3, 12T28 x 2, 24T27 $64$: 16T76 $96$: 12T48, 12T53 x 2, 24T146 $192$: $V_4^2:(S_3\times C_2)$, 12T86 x 2, 24T337, 24T397 $384$: 12T136, 24T1070 $768$: 12T186, 24T1595, 24T1599, 24T1719 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 3: $S_3$
Degree 4: $C_2^2$
Degree 6: $D_{6}$ x 3
Degree 8: None
Degree 12: $S_3 \times C_2^2$
Low degree siblings
24T5391 x 3, 24T5464 x 4, 24T6155 x 4, 24T6590 x 4, 32T205914 x 4, 32T206196 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
Conjugacy classes not computed
Character table
86 x 86 character table
Regular extensions
Data not computed