Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1764$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,2,3)(5,16,7,14)(6,15,8,13)(9,11)(10,12), (1,12,14,3,10,16)(2,11,13,4,9,15) | |
| $|\Aut(F/K)|$: | $2$ |
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: 32T397259 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$
Low degree siblings
16T1761 x 8, 16T1764 x 7, 32T720618 x 4, 32T720619 x 4, 32T720620 x 4, 32T720621 x 4, 32T720622 x 8, 32T720623 x 4, 32T720624 x 4, 32T720627 x 4, 32T720628 x 4, 32T720629 x 4, 32T720630 x 4, 32T720631 x 4, 32T720632 x 4Siblings 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. |