Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,14,19,6)(2,4,13,20,5)(7,11,9,21,16)(8,12,10,22,15)(17,18), (1,11,3,5,22,18,7,16,13,20)(2,12,4,6,21,17,8,15,14,19)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 10: $C_{10}$ x 3 20: 20T3 110: $F_{11}$ 220: 22T6 112640: 22T34 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $F_{11}$
Low degree siblings
22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $225280=2^{12} \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |