Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $45$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,40)(2,39)(3,13,29,23,17,25,31,4,14,30,24,18,26,32)(5,15,45,7,41,28,10,33,36,44,21,12,38,20)(6,16,46,8,42,27,9,34,35,43,22,11,37,19), (1,44,30)(2,43,29)(3,10,27,19,17,24,26)(4,9,28,20,18,23,25)(5,40,8,41,16,45,21,38,14,34,11,31)(6,39,7,42,15,46,22,37,13,33,12,32) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 25852016738884976640000: $S_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: $S_{23}$
Low degree siblings
46T45Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 2,510 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $51704033477769953280000=2^{20} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |