Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $35$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,15,22,3,11,34,14,27,32,19,10,39,42,36,8,46,24,43,29,26,37)(2,17,16,21,4,12,33,13,28,31,20,9,40,41,35,7,45,23,44,30,25,38), (1,26,30,45,18,43,10,11,19,6,42,2,25,29,46,17,44,9,12,20,5,41)(3,34,15,36,24,21,14,28,37,32,8,4,33,16,35,23,22,13,27,38,31,7) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 11: $C_{11}$ 22: 22T1 506: $F_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $F_{23}$
Low degree siblings
46T36Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 8,624 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2122317824=2^{23} \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |