Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $289$ | |
| CHM label : | $[S(3)^{4}]S(4)=S(3)wrS(4)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (4,8), (1,10)(2,5)(6,9), (4,8,12), (1,4,7,10)(2,5,8,11)(3,6,9,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ 48: $S_4\times C_2$ 192: $V_4^2:(S_3\times C_2)$ 384: $C_2 \wr S_4$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: $S_4$
Degree 6: None
Low degree siblings
24T14025, 24T14026, 24T14027, 24T14028, 24T14029, 24T14030, 24T14031, 24T14032, 24T14043, 36T13625, 36T13642Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 51 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $31104=2^{7} \cdot 3^{5}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |