Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $46$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,37,3,25,15)(2,38,4,26,16)(5,18,45,10,40,34,11,7,6,17,46,9,39,33,12,8)(13,14)(19,28,36,43)(20,27,35,44)(21,24,22,23)(29,32,30,31), (1,23,6)(2,24,5)(3,38,45,29,9,42,12,35,31,25,14,18,43,7,33,27,40,19,15)(4,37,46,30,10,41,11,36,32,26,13,17,44,8,34,28,39,20,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 12926008369442488320000: $A_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $A_{23}$
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 17,144 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $54215608607986106530529280000=2^{40} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |