Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1537$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,16,11,2,7,15,12)(3,5,13,9,4,6,14,10), (1,12,15,4,9,13)(2,11,16,3,10,14)(5,6)(7,8) | |
| $|\Aut(F/K)|$: | $4$ |
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: $Q_8:S_4$ x 2, $V_4^2:(S_3\times C_2)$ x 2, 12T100 384: $C_2 \wr S_4$ x 2, 16T741 768: 16T1068 1536: 24T3296, 24T3382 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $Q_8:S_4$, $C_2 \wr S_4$ x 2
Low degree siblings
16T1537 x 15, 32T205678 x 4, 32T205679 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3072=2^{10} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |