Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $42$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,8)(2,7)(3,14)(4,13)(5,10)(6,9)(15,20,16,19)(17,18)(21,22), (3,9,17,19,22,4,10,18,20,21)(5,14,16,11,7)(6,13,15,12,8) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $660$: $\PSL(2,11)$ $1320$: 22T13 $675840$: 22T39 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $\PSL(2,11)$
Low degree siblings
22T42, 44T433 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 112 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1351680=2^{13} \cdot 3 \cdot 5 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |