Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $26$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,44,29,38,40,5,31,3,19,23)(2,7,43,30,37,39,6,32,4,20,24)(11,22,36,28,26,14,34,15,45,42,17,12,21,35,27,25,13,33,16,46,41,18), (1,27,40,41,4,35,25,32,10,13,29,2,28,39,42,3,36,26,31,9,14,30)(5,43,12,21,16,37,34,18,45,19,7)(6,44,11,22,15,38,33,17,46,20,8) | |
| $|\Aut(F/K)|$: | $2$ |
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 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 64 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1036288=2^{12} \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |