Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1871$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,10,6,16,8,14,3,12,2,9,5,15,7,13,4,11), (1,16,2,15)(3,12)(4,11)(5,9)(6,10)(7,14,8,13) | |
| $|\Aut(F/K)|$: | $2$ |
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: $S_4\wr C_2$ x 3 18432: 16T1793 36864: 32T1515321 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1871 x 3, 32T1831797 x 2, 32T1831798 x 2, 32T1831799 x 2, 32T1831874 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 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. |