Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $23$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,32,5,40,11,29,20,24,22,28,2,34,18,43,19,45,9,25,17,41,6,42)(3,36,8,46,4,38,21,26,12,31,10,27,7,44,14,35,13,33,23,30,15,37)(16,39), (1,10,8,11,18,19,6,14,2,20,16,22,13,15,12,5,4,17,9,21,3,7)(24,33,38,28,25,31,42,43,41,45,37,30,44,39,26,29,46,35,34,36,32,40) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 11: $C_{11}$ 22: $D_{11}$, 22T1 x 3 44: $D_{22}$, 44T2 242: 22T7 484: 44T27 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 169 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $256036=2^{2} \cdot 11^{2} \cdot 23^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |