Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1760$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,12,7,3,14,9,6)(2,15,11,8,4,13,10,5), (1,14,2,13)(3,15,4,16)(9,10) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4$ 48: $S_4\times C_2$, $\textrm{GL(2,3)}$ x 2 96: 16T188 192: $V_4^2:(S_3\times C_2)$ 384: $C_2 \wr S_4$ x 2, 24T819 768: 16T1066 1536: 32T97075 6144: 48T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$
Low degree siblings
16T1760 x 15, 32T720611 x 8, 32T720612 x 8, 32T720613 x 8, 32T720614 x 8, 32T720615 x 8, 32T720616 x 8, 32T720617 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 64 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. |