Group action invariants
| Degree $n$ : | $13$ | |
| Transitive number $t$ : | $9$ | |
| Group : | $S_{13}$ | |
| CHM label : | $S13$ | |
| Parity: | $-1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2,3,4,5,6,7,8,9,10,11,12,13), (1,2) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Prime degree - none
Low degree siblings
26T83Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 101 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6227020800=2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |