Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1758$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,12,4,15,10)(2,14,11,3,16,9)(7,8), (1,6,9,15,4,7,12,14,2,5,10,16,3,8,11,13), (5,14,11,8,16,10,6,13,12,7,15,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $D_{4}$ x 2, $C_2^3$ 12: $D_{6}$ x 3 16: $D_4\times C_2$ 24: $S_4$, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 3, 12T28 96: 12T48 192: $V_4^2:(S_3\times C_2)$, 12T86 384: $C_2 \wr S_4$ x 2, 12T136 768: 12T186, 16T1045, 16T1049 1536: 32T96912 3072: 24T7075 6144: 24T9145 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$
Low degree siblings
16T1758 x 15, 32T720590 x 8, 32T720591 x 8, 32T720592 x 8, 32T720593 x 8, 32T720594 x 8, 32T720595 x 8, 32T720596 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 93 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. |