Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $231$ | |
| CHM label : | $[3^{4}]S(4)=3wrS(4)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10)(2,5)(6,9), (4,8,12), (1,4,7,10)(2,5,8,11)(3,6,9,12) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $S_3$, $C_6$ 18: $S_3\times C_3$ 24: $S_4$ 72: 12T45 648: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: $S_4$
Degree 6: None
Low degree siblings
12T231, 18T349, 24T4949 x 2, 24T4955 x 2, 27T400, 36T2775, 36T2776 x 2, 36T2847, 36T2849 x 2, 36T2985Siblings 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: | $1944=2^{3} \cdot 3^{5}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1944, 3876] |
| Character table: Data not available. |