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Group invariants
| Abstract group: | $C_4^3:C_2^2:S_4$ |
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| Order: | $6144=2^{11} \cdot 3$ |
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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 $t$: | $9232$ |
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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: | $(7,8)(9,23)(10,24)(11,21)(12,22)(13,17)(14,18)(15,19)(16,20)$, $(1,16,5,10,2,15,6,9)(3,14,8,11,4,13,7,12)(17,21,20,24)(18,22,19,23)$, $(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15)(17,20,18,19)(21,24,22,23)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $6$: $S_3$ $8$: $D_{4}$ x 6, $C_2^3$ $12$: $D_{6}$ x 3 $16$: $D_4\times C_2$ x 3 $24$: $S_4$, $S_3 \times C_2^2$, $(C_6\times C_2):C_2$ x 2 $32$: $C_2^2 \wr C_2$ $48$: $S_4\times C_2$ x 3, 12T28 x 2, 24T25 $96$: 12T48, 12T49 x 2, 24T145 $192$: $V_4^2:(S_3\times C_2)$, 12T86 x 2, 24T398 $384$: 12T136, 24T1072 $768$: 24T1558, 24T1595 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $S_3$
Degree 4: None
Degree 6: $S_4$
Degree 8: None
Degree 12: 12T137
Low degree siblings
24T9230 x 8, 24T9232 x 7Siblings 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
72 x 72 character table
Regular extensions
Data not computed