Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $49$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,37,18)(2,38,17)(3,35,10,8)(4,36,9,7)(5,43,20,30,27,40,25,42,22,23,46,31,15,11,6,44,19,29,28,39,26,41,21,24,45,32,16,12)(13,33,14,34), (1,23,20,46,40,31,10,15,27,22,18,12,25,7,38,2,24,19,45,39,32,9,16,28,21,17,11,26,8,37)(3,44,6,33,30,35,42,13,4,43,5,34,29,36,41,14) |
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
46T48Siblings 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: | not available |
| Character table: not available. |