Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $50$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,39,14,46,36,7,11)(2,30,40,13,45,35,8,12)(3,32,16,18,27,44,21,25,5,37,24,20,41,4,31,15,17,28,43,22,26,6,38,23,19,42)(9,34)(10,33), (3,35,22,30,45,8,44,27,17,40,19,14,42,23,5,33,10,25,15,11,37,32)(4,36,21,29,46,7,43,28,18,39,20,13,41,24,6,34,9,26,16,12,38,31) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 25852016738884976640000: $S_{23}$ 51704033477769953280000: 46T45 108431217215972213061058560000: 46T48 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $S_{23}$
Low degree siblings
46T50Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 68,150 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $216862434431944426122117120000=2^{42} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |