Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $44$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,10,18,11,15,5,4,2,22,9,17,12,16,6,3)(7,8)(13,19)(14,20), (1,15,7,13,11,10,17,4,2,16,8,14,12,9,18,3)(5,19)(6,20) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 7920: $M_{11}$ 15840: 22T26 8110080: 22T43 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $M_{11}$
Low degree siblings
22T44, 44T613, 44T615 x 2, 44T617 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $16220160=2^{15} \cdot 3^{2} \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |