Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $49$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,16,13,6,3,10,22)(2,15,14,5,4,9,21)(7,11)(8,12)(17,20)(18,19), (1,17,3,10,12,6,7,2,18,4,9,11,5,8)(13,19,15)(14,20,16)(21,22) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $19958400$: $A_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $A_{11}$
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 200 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $20437401600=2^{17} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |