Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $46$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,5,13,21,19,18,7,16,9,11,4)(2,6,14,22,20,17,8,15,10,12,3), (1,2)(3,4)(5,15,19,14,11,22,7,17,9,6,16,20,13,12,21,8,18,10) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19958400$: $A_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
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 62 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |