Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1665$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,2,12)(3,7)(4,8)(5,9,6,10)(13,16)(14,15), (1,3,15,2,4,16)(7,8)(9,14,12)(10,13,11), (1,8,4,11,6,9,2,7,3,12,5,10)(13,15,14,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $C_2^3$ 12: $D_{6}$ x 3 24: $S_4$ x 3, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 9 96: $V_4^2:S_3$, 12T48 x 3 192: $C_2^3:S_4$ x 4, 12T100 x 3 384: 12T139, 16T747 x 6 768: 32T34907 1536: 16T1301 3072: 24T5981 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $S_4$
Degree 8: $S_4\times C_2$
Low degree siblings
16T1659 x 4, 16T1665 x 3, 32T397402 x 4, 32T397403 x 4, 32T397404 x 2, 32T397405 x 4, 32T397406 x 2, 32T397422 x 2, 32T397423 x 2, 32T397424 x 2, 32T397425 x 2, 32T397426 x 2, 32T397427 x 2, 32T397728 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 78 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6144=2^{11} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |