Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $36$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,15,5,10,4,2,16,6,9,3)(7,17,14,19,22,8,18,13,20,21)(11,12), (1,6,19,14,4)(2,5,20,13,3)(7,15,21,10,12,8,16,22,9,11) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $10$: $C_{10}$ $55$: $C_{11}:C_5$ $110$: 22T5 $56320$: 22T33 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $C_{11}:C_5$
Low degree siblings
22T36 x 2, 44T314 x 3, 44T315 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 80 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $112640=2^{11} \cdot 5 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |