Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1675$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,5,15,4,6,16)(7,14,9)(8,13,10)(11,12), (1,10,2,9)(3,11,4,12)(5,14)(6,13)(7,15,8,16), (1,15,3,5)(2,16,4,6)(7,11,14,10,8,12,13,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 8: $D_{4}$ 12: $D_{6}$ 24: $S_4$, $D_{12}$ 48: $S_4\times C_2$ 96: 12T54 192: $V_4^2:(S_3\times C_2)$ 384: $C_2 \wr S_4$, 12T152, 16T753 768: 32T34843 1536: 16T1313 3072: 24T5962 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
16T1675 x 3, 16T1682 x 4, 32T397453 x 2, 32T397454 x 2, 32T397455 x 4, 32T397456 x 2, 32T397457 x 2, 32T397458 x 2, 32T397459 x 2, 32T397483 x 2, 32T397484 x 2, 32T397757 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 54 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. |