Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $30$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,22,19,17,15,14,11,10,7,6,4)(2,21,20,18,16,13,12,9,8,5,3), (1,9)(2,10)(3,7)(4,8)(11,22,12,21)(13,20)(14,19)(15,17,16,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 22: $D_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $D_{11}$
Low degree siblings
22T29 x 31, 22T30 x 30, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 100 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $22528=2^{11} \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |