Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1884$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,5,12,16,14,4,9)(2,8,6,11,15,13,3,10), (3,5,15,4,6,16)(7,8)(9,11,13)(10,12,14), (1,8,2,7)(3,14,15,12,6,9,4,13,16,11,5,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 72: $C_3^2:D_4$ 144: 12T77 1152: $S_4\wr C_2$ 2304: 12T235 36864: 16T1829 73728: 32T1832104 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1884 x 7, 32T2076186 x 4, 32T2076187 x 4, 32T2076188 x 4, 32T2076189 x 4, 32T2076190 x 4, 32T2076191 x 4, 32T2076192 x 4, 32T2076378 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 136 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. |