Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1945$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,2,15)(3,8,9,13,6)(4,7,10,14,5)(11,12), (1,10,8,15,13)(2,9,7,16,14)(3,11,5)(4,12,6) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 40320: $S_8$ 2580480: 56T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 8: $S_8$
Low degree siblings
16T1945, 32T2711885Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 100 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5160960=2^{14} \cdot 3^{2} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |