Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $52$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14)(2,13)(3,9,16,8,19)(4,10,15,7,20)(5,18,6,17), (1,10,21,19,4,15,11)(2,9,22,20,3,16,12)(5,8,14,6,7,13)(17,18) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 19958400: $A_{11}$ 39916800: 22T46 20437401600: 22T49 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $A_{11}$
Low degree siblings
44T1750Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 400 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. |