Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1887$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14)(2,13)(3,10,15,11,6,8,4,9,16,12,5,7), (1,5,3,15)(2,6,4,16)(7,11,13,9,8,12,14,10), (1,13)(2,14)(3,7,4,8)(5,10)(6,9)(11,16)(12,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ x 2 8: $D_{4}$ x 2, $C_2^3$ 12: $D_{6}$ x 6 16: $D_4\times C_2$ 24: $S_3 \times C_2^2$ x 2 36: $S_3^2$ 48: 12T28 x 2 72: 12T37 144: 12T81 576: $(A_4\wr C_2):C_2$ 1152: 12T195 2304: 12T240 36864: 16T1827 73728: 32T1832161 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
16T1887 x 7, 32T2076207 x 4, 32T2076208 x 4, 32T2076209 x 4, 32T2076210 x 4, 32T2076211 x 4, 32T2076212 x 4, 32T2076213 x 4, 32T2076357 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 148 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $147456=2^{14} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |