Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $50$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,13,7,22,9,12,17,4,14,8,21,10,11,18)(5,6)(15,20,16,19), (1,4,21,19,7,2,3,22,20,8)(5,17,15,11,6,18,16,12)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
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
22T51, 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. |