Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $39$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,12,13,17,2,10,11,14,18)(3,22,19,6,8)(4,21,20,5,7)(15,16), (1,7,6,2,8,5)(3,4)(9,21,18)(10,22,17)(11,15,13,12,16,14)(19,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 660: $\PSL(2,11)$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $\PSL(2,11)$
Low degree siblings
22T39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $675840=2^{12} \cdot 3 \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |