Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1683$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,13,8,2,9,14,7)(3,12,16,6,4,11,15,5), (1,7,9,2,8,10)(3,6,12,4,5,11)(13,15)(14,16) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4$, $(C_6\times C_2):C_2$ 48: $S_4\times C_2$ 96: 12T49 192: $V_4^2:(S_3\times C_2)$ 384: $C_2 \wr S_4$, 12T145, 16T745 x 2, 16T755 768: 32T34844 1536: 16T1315 3072: 24T5585 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$
Low degree siblings
16T1676 x 4, 16T1683 x 3, 32T397460 x 4, 32T397461 x 2, 32T397462 x 2, 32T397463 x 2, 32T397464 x 2, 32T397465 x 2, 32T397466 x 2, 32T397485 x 2, 32T397486 x 2, 32T397725 x 2Siblings 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: | $6144=2^{11} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |