Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $11$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,13,46,2,40,14,34,3,28,15,45,4,39,16,33,5,27,17,44,6,38,18,32,7,26,19,43,8,37,20,31,9,25,21,42,10,36,22,30,11,24,23,41,12,35), (1,9,15,8,20,6,7,2,4,17,21)(3,22,19,11,5,12,23,14,13,18,16)(24,40,46,31,34,38,28,30,25,26,35)(27,44,36,33,29,39,37,42,41,32,43) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 22: $D_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
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 64 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $11638=2 \cdot 11 \cdot 23^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |