Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1872$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15)(2,16)(3,14,5,12,4,13,6,11)(7,9)(8,10), (1,14,5,15,8,11,2,13,6,16,7,12)(3,9,4,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 72: $C_3^2:D_4$ 1152: $S_4\wr C_2$ 18432: 16T1792 36864: 32T1515323 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1872 x 3, 32T1831800 x 2, 32T1831801 x 2, 32T1831802 x 2, 32T1831954 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $73728=2^{13} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |