Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1870$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,16,3)(2,6,15,4)(7,14,9,11,8,13,10,12), (1,9,6,11,15,7)(2,10,5,12,16,8)(3,13,4,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ x 2 8: $D_{4}$ 12: $D_{6}$ x 2 24: $D_{12}$, $(C_6\times C_2):C_2$ 36: $S_3^2$ 72: 12T38 576: $(A_4\wr C_2):C_2$ 1152: 12T196 18432: 16T1795 36864: 32T1515339 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $(A_4\wr C_2):C_2$
Low degree siblings
16T1870 x 3, 32T1831794 x 2, 32T1831795 x 2, 32T1831796 x 2, 32T1831924 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 83 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. |