Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $23$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,21,10,19,8,18,6,15,3,14)(2,12,22,9,20,7,17,5,16,4,13), (1,4,6,8,10,12,14,15,17,20,21)(2,3,5,7,9,11,13,16,18,19,22) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 11: $C_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: $C_{11}$
Low degree siblings
22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $11264=2^{10} \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |