Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $7$ | |
| Group : | $C_{11}\times D_{11}$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,6,16,11,18,5,20,10,22,4,13,9,15,3,17,8,19,2,21,7,12), (1,14)(2,21)(3,17)(4,13)(5,20)(6,16)(7,12)(8,19)(9,15)(10,22)(11,18) | |
| $|\Aut(F/K)|$: | $11$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 11: $C_{11}$ 22: $D_{11}$, 22T1 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
22T7 x 4Siblings 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: | $242=2 \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [242, 3] |
| Character table: Data not available. |