Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1862$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,9,3,7,6,11)(2,10,4,8,5,12)(13,16)(14,15), (1,6)(2,5)(3,16,4,15)(7,13,11)(8,14,12)(9,10), (1,15,5)(2,16,6)(3,4)(9,10)(11,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $S_3$, $C_6$ x 3 8: $D_{4}$ 12: $D_{6}$, $C_6\times C_2$ 18: $S_3\times C_3$ 24: $(C_6\times C_2):C_2$, $D_4 \times C_3$ 36: $C_6\times S_3$ 72: 12T42 288: $A_4\wr C_2$ 576: 12T158 1152: 12T208 18432: 16T1783 36864: 32T1515348 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $A_4\wr C_2$
Low degree siblings
16T1862 x 3, 32T1831766 x 2, 32T1831767 x 2, 32T1831768 x 2, 32T1831936 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 152 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. |