Group action invariants
| Degree $n$ : | $12$ | |
| Transitive number $t$ : | $299$ | |
| Group : | $S_6\wr C_2$ | |
| CHM label : | $[S(6)^{2}]2=S(6)wr2$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (2,4,6,8,10,12), (2,12), (1,12)(2,3)(4,5)(6,7)(8,9)(10,11) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 4: None
Degree 6: None
Low degree siblings
12T299, 20T973, 24T21434 x 2, 24T21435 x 2, 24T21436 x 2, 30T2029 x 2, 36T36499 x 2, 40T148363 x 2, 40T148364, 40T148365 x 2, 40T148366, 40T148367Siblings 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: | $1036800=2^{9} \cdot 3^{4} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |