Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $42$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,46,5,36,2,40,18,33,17,44,19,35,9,24)(3,42,10,30,20,25,14,43,7,29,6,37,13,34)(4,39,22,32,15,27,23,26,21,41,11,31,8,28)(12,38)(16,45), (1,21,4,17,6,15,5,18,10,8,13,2,16,23)(3,20,12,11,7,19,14)(9,22)(24,45,30,35,37,27,43)(25,46,38,40,41,36,42)(26,32,31,28,34,33,29) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ 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 170 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $208119169843200=2^{15} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \cdot 23^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |