Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $57$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,10,15,4,16,3,22,9,13,8,21)(2,19,6,14,7,18)(5,17,11,20), (1,19,11,22,9,18)(2,15,4,21,3,16,8,13,10,20,7,17,5,14,6,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T1966, 44T1967, 44T1968Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 1,652 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3186701844480000=2^{17} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |