Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $39$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,42)(2,41)(3,25,10,46,13,6,4,26,9,45,14,5)(7,22,15)(8,21,16)(11,12)(17,38,27)(18,37,28)(19,33,36,40,43,23)(20,34,35,39,44,24)(29,31,30,32), (1,45,42,26,30,44,34,39,3,5,35,21,12,13,24,10,38,28,8,19,16,31,18)(2,46,41,25,29,43,33,40,4,6,36,22,11,14,23,9,37,27,7,20,15,32,17) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $10200960$: $M_{23}$ $20401920$: 46T27 $20891566080$: 46T38 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 120 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $41783132160=2^{19} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |