Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $44$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,26,28,10,40,14,15,32,2,6,25,27,9,39,13,16,31)(3,17,29,8)(4,18,30,7)(11,20,33,37)(12,19,34,38)(21,23,35,46,41,43)(22,24,36,45,42,44), (1,29,18,26,16,19,27,6,11,32,42,36)(2,30,17,25,15,20,28,5,12,31,41,35)(3,39)(4,40)(7,14,23,38,22,46)(8,13,24,37,21,45)(9,44)(10,43) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_{23}$
Low degree siblings
23T7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 1,255 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |