Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1948$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,11,3,6,14,15,10)(2,7,12,4,5,13,16,9), (1,13,12,16)(2,14,11,15)(7,9)(8,10), (1,2)(3,16,9,14,8,12)(4,15,10,13,7,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 40320: $S_8$ 80640: 16T1873 5160960: 56T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: None
Degree 8: $S_8$
Low degree siblings
16T1948 x 3, 32T2746190 x 2, 32T2746191 x 2, 32T2746192 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 185 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $10321920=2^{15} \cdot 3^{2} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |