Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $293$ | |
| CHM label : | $[2^{6}]S(6)=2wrS(6)$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,3)(2,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 720: $S_6$ 1440: $S_6\times C_2$ 23040: 30T937 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 4: None
Degree 6: $S_6$
Low degree siblings
12T293 x 3, 24T14632 x 2, 24T14633 x 2, 24T14634 x 2, 40T18563 x 2, 40T18564 x 2, 40T18573 x 2, 40T18579 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $46080=2^{10} \cdot 3^{2} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |