Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $47$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,14,23,5,18,19,31,26,15,12,34,2,8,13,24,6,17,20,32,25,16,11,33)(3,38,44,9)(4,37,43,10)(21,40,46,30,22,39,45,29)(27,35,28,36), (1,45,11,41,37,22,26,39,16,36,28,34,32,30,20,6,17)(2,46,12,42,38,21,25,40,15,35,27,33,31,29,19,5,18)(3,44,14,9,23)(4,43,13,10,24) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 12926008369442488320000: $A_{23}$ 25852016738884976640000: 46T43 54215608607986106530529280000: 46T46 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 34,288 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. |