Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $43$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,36,14,39)(2,35,13,40)(3,24,27,12,15,38,42,5,19,8,34,44)(4,23,28,11,16,37,41,6,20,7,33,43)(9,30,31,21,18,26,46)(10,29,32,22,17,25,45), (1,19,33,13,45,18,36,44,16,12,23,5,7,38,25,3,10,27,39,2,20,34,14,46,17,35,43,15,11,24,6,8,37,26,4,9,28,40)(21,41)(22,42)(29,31)(30,32) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $12926008369442488320000$: $A_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
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 1,282 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |