Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $34$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,34,12,29,31,22,25,5,14,20,35)(2,33,11,30,32,21,26,6,13,19,36)(3,24,15,9,40,28,41,17,45,43,7,4,23,16,10,39,27,42,18,46,44,8), (1,32,24,20,17,39,28,21,42,6,33)(2,31,23,19,18,40,27,22,41,5,34)(3,10,36,25,43,30,45,7,11,13,37,4,9,35,26,44,29,46,8,12,14,38) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 11: $C_{11}$ 22: 22T1 253: $C_{23}:C_{11}$ 506: 46T4 518144: 46T25 x 2 1036288: 46T26 x 2 1061158912: 46T33 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $C_{23}:C_{11}$
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 33,248 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. |