Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1806$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,3)(2,5,4)(7,12,13,8,11,14), (1,14,2,13)(3,11,6,8,16,10,4,12,5,7,15,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 8: $D_{4}$ 12: $A_4$, $C_6\times C_2$ 24: $A_4\times C_2$ x 3, $D_4 \times C_3$ 48: $C_2^2 \times A_4$ 96: $C_2^4:C_6$, 12T51 192: 12T87 384: 12T134 1536: 16T1299 6144: 16T1655 12288: 32T723243 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $C_2^4:C_6$
Low degree siblings
16T1806 x 3, 32T1120285 x 2, 32T1120286 x 2, 32T1120287 x 2, 32T1120480 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $24576=2^{13} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |