Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1916$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,12,13,3,16,2,7,11,14,4,15)(5,10,6,9), (1,2)(3,16,7,5,10,11,13)(4,15,8,6,9,12,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 168: $\GL(3,2)$ 336: 14T17 1344: $C_2^3:\GL(3,2)$ 2688: 14T43 21504: 16T1801 172032: 56T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 8: $C_2^3:\GL(3,2)$
Low degree siblings
16T1916, 32T2267427Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 79 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $344064=2^{14} \cdot 3 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |