Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $42$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8)(2,7)(3,14)(4,13)(5,10)(6,9)(15,20,16,19)(17,18)(21,22), (3,9,17,19,22,4,10,18,20,21)(5,14,16,11,7)(6,13,15,12,8) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 660: $\PSL(2,11)$ 1320: 22T13 675840: 22T39 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $\PSL(2,11)$
Low degree siblings
22T42, 44T433 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 112 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1351680=2^{13} \cdot 3 \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |