Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1086$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(3,4), (1,7,2,8)(3,5,4,6)(9,15,10,16)(11,14,12,13), (1,14,8,16,2,13,7,15)(3,11,5,10,4,12,6,9), (9,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_4$ x 8, $C_2^2$ x 35 8: $D_{4}$ x 56, $C_4\times C_2$ x 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 84, $C_2^2:C_4$ x 112, $C_4\times C_2^2$ x 14, $C_2^4$ 32: $C_2^2 \wr C_2$ x 112, $C_2 \times (C_2^2:C_4)$ x 84, $C_2^2 \times D_4$ x 14, 32T34 64: 16T79 x 56, 16T105 x 28, 32T262 x 7 128: 16T325 x 8, 32T1149 x 7 256: 32T5587 512: 32T22451 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 8: $C_2^2:C_4$
Low degree siblings
16T1086 x 15, 16T1100 x 32, 32T35289 x 32, 32T35290 x 32, 32T35291 x 32, 32T35292 x 16, 32T35293 x 32, 32T35294 x 16, 32T35295 x 8, 32T35296 x 32, 32T35297 x 8, 32T35298 x 8, 32T35299 x 8, 32T35300 x 16, 32T35301 x 8, 32T35302 x 8, 32T35303 x 8, 32T35416 x 32, 32T35417 x 32, 32T35418 x 32, 32T35419 x 32, 32T35420 x 32, 32T35421 x 16, 32T35422 x 16, 32T35423 x 32, 32T35424 x 32, 32T35425 x 32, 32T35426 x 32, 32T35427 x 16, 32T35428 x 16, 32T35429 x 32, 32T35430 x 32, 32T35431 x 32, 32T35432 x 16, 32T35433 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 97 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |