Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $48$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,45,32,29,19,9,18,42,7,35,37)(2,16,46,31,30,20,10,17,41,8,36,38)(3,43,40,5,12)(4,44,39,6,11)(13,21,34)(14,22,33)(23,27,26,24,28,25), (1,45,6,27,23,41,35,15,20,30,4,11,14,9,34,37,43,7,2,46,5,28,24,42,36,16,19,29,3,12,13,10,33,38,44,8)(17,31,21,26,18,32,22,25) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 25852016738884976640000: $S_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $S_{23}$
Low degree siblings
46T49Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 34,075 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $108431217215972213061058560000=2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |