Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $40$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,38,42,36,2,30,37,41,35)(3,10,39,19,32)(4,9,40,20,31)(5,23,27,7,46,6,24,28,8,45)(11,12)(13,17,21,43,16)(14,18,22,44,15)(25,26), (1,41,25,5,17,20,32,15,33,38,43,22,13,7,36,2,42,26,6,18,19,31,16,34,37,44,21,14,8,35)(3,11,27,45,24)(4,12,28,46,23)(9,29,40,10,30,39) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 10200960: $M_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $M_{23}$
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 368 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $42785927331840=2^{29} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |