Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1765$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,6,14)(2,12,5,13)(3,15,8,9)(4,16,7,10), (1,8,4)(2,7,3)(9,16,14,10,15,13)(11,12), (1,6,8,4)(2,5,7,3)(9,12)(10,11)(13,14)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: $V_4^2:(S_3\times C_2)$ x 6, 12T100 768: 16T1068 x 3 3072: 16T1526 6144: 32T398944 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $V_4^2:(S_3\times C_2)$
Low degree siblings
16T1765 x 5, 32T720633 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 74 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $12288=2^{12} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |