Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1435$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,13,2,14)(3,12,8,16)(4,11,7,15)(5,9,6,10), (1,6,2,5)(7,8)(9,13)(10,14)(11,12)(15,16), (1,12)(2,11)(3,13,8,9)(4,14,7,10)(5,15)(6,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 4, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 2, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 4, $C_4\times C_2^2$ 32: $C_2^3 : C_4 $ x 4, $C_4^2:C_2$ x 2, $C_2 \times (C_2^2:C_4)$, 16T37 x 4 64: 16T76 x 2, 32T197 128: 16T212 x 2, 16T274 256: 32T3799 512: 16T813 x 2, 16T825 1024: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $C_2^3: C_4$
Low degree siblings
16T1372 x 8, 16T1435 x 7, 32T98243 x 4, 32T98244 x 16, 32T98245 x 8, 32T98246 x 8, 32T98247 x 8, 32T98248 x 8, 32T98249 x 4, 32T98250 x 4, 32T98251 x 8, 32T98252 x 16, 32T98253 x 4, 32T98254 x 8, 32T98255 x 8, 32T98256 x 8, 32T98257 x 8, 32T98258 x 4, 32T98259 x 4, 32T98960 x 4, 32T98961 x 8, 32T98962 x 8, 32T98963 x 4, 32T98964 x 8, 32T98965 x 8, 32T98966 x 4, 32T98967 x 4, 32T98968 x 4, 32T98969 x 4, 32T110417 x 8, 32T110418 x 8, 32T112054 x 4, 32T112055 x 4, 32T115627 x 8, 32T138587 x 2, 32T138604 x 2, 32T165886 x 2, 32T190950 x 2, 32T200519 x 2, 32T204240 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2048=2^{11}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |