Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $44$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| 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) |
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: | not available |
| Character table: not available. |