Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $292$ | |
| CHM label : | $[S(4)^{3}]3=S(4)wr3$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,6,9,12), (6,9), (1,5,9)(2,6,10)(3,7,11)(4,8,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ 24: $A_4\times C_2$ 648: $S_3 \wr C_3 $ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 4: None
Degree 6: None
Low degree siblings
18T702 x 2, 18T703, 18T706 x 2, 18T707, 18T708, 18T709, 24T14599 x 2, 24T14600, 24T14601 x 2, 24T14602, 24T14603, 36T15293 x 2, 36T15294 x 2, 36T15295 x 2, 36T15296 x 2, 36T15298 x 2, 36T15299 x 2, 36T15300 x 2, 36T15301 x 2, 36T15316, 36T15317, 36T15318 x 2, 36T15324, 36T15325, 36T15326, 36T15327, 36T15334, 36T15335, 36T15336 x 2, 36T15793, 36T15794, 36T15795 x 2, 36T15804 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $41472=2^{9} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |