Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $36$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,25,28,32,40,10,42,14,3,29,36)(2,26,27,31,39,9,41,13,4,30,35)(5,34,44,18,11,45,21,20,15,8,38,6,33,43,17,12,46,22,19,16,7,37)(23,24), (1,26,23,28,20,36,4,22,31,11,6,18,40,41,37,45,29,16,43,34,8,14)(2,25,24,27,19,35,3,21,32,12,5,17,39,42,38,46,30,15,44,33,7,13)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
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
46T35Siblings 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. |