Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $47$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,20,22,18,7,4,16,10,11,6,2,14,19,21,17,8,3,15,9,12,5), (1,15,10,8,6,20,12)(2,16,9,7,5,19,11)(3,17,22,13)(4,18,21,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 39916800: $S_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: $S_{11}$
Low degree siblings
22T47, 44T1258Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 112 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $79833600=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |