Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $45$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,22,20,18,4,7,9,11,5,14)(2,21,19,17,3,8,10,12,6,13)(15,16), (1,4,20,12,9,17,5)(2,3,19,11,10,18,6)(7,15,14)(8,16,13) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: $S_{11}$
Low degree siblings
11T8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 56 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. |