Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $51$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,5,21,11,7,10)(2,13,6,22,12,8,9)(3,19)(4,20)(15,16)(17,18), (1,17,11,3,13,5,16)(2,18,12,4,14,6,15)(7,19,22,10)(8,20,21,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 39916800: $S_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $S_{11}$
Low degree siblings
22T50, 44T1749Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 376 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |