Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $41$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,39,24,31,34,29,11)(2,40,23,32,33,30,12)(3,42,22,36,26,5,46,44,7,15,17,27,14,20)(4,41,21,35,25,6,45,43,8,16,18,28,13,19)(9,37,10,38), (1,6,22,10,3,42,38,44,39,17,30,2,5,21,9,4,41,37,43,40,18,29)(7,45,20,27,11,34,16,25,13,24,31)(8,46,19,28,12,33,15,26,14,23,32) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 10200960: $M_{23}$ 20401920: 46T27 42785927331840: 46T40 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 736 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $85571854663680=2^{30} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |