Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $301$ | |
| Group : | $S_{12}$ | |
| CHM label : | $S12$ | |
| Parity: | $-1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2), (1,2,3,4,5,6,7,8,9,10,11,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: None
Degree 6: None
Low degree siblings
24T24748Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $479001600=2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |