Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1666$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,13,4,6,16)(2,8,14,3,5,15)(9,10), (1,15,9,5,3,13,11,8,2,16,10,6,4,14,12,7), (1,8,15,10,2,7,16,9)(3,5,14,12,4,6,13,11) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4$, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 3 96: 12T48 192: $V_4^2:(S_3\times C_2)$ 384: $C_2 \wr S_4$ x 2, 12T136 768: 16T1045 1536: 24T4549 3072: 24T6624 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$
Low degree siblings
16T1666 x 7, 32T397428 x 4, 32T397429 x 8, 32T397430 x 4, 32T397431 x 8, 32T397432 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 63 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. |