Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $43$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,21,17,20)(2,22,18,19)(3,5,8,16,4,6,7,15)(9,10)(11,12)(13,14), (1,9,16,19,14,12,18,4,6,22,8)(2,10,15,20,13,11,17,3,5,21,7) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $7920$: $M_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $M_{11}$
Low degree siblings
22T43, 44T554Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 52 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8110080=2^{14} \cdot 3^{2} \cdot 5 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |