Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $29$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,13,4,16,6,17,8,19,9,22,11)(2,14,3,15,5,18,7,20,10,21,12), (1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16,8,15)(9,13)(10,14) |
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 30, 22T30 x 31, 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: | not available |
| Character table: not available. |