Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1102$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(7,8), (1,3,5,16)(2,4,6,15)(7,9,11,14)(8,10,12,13), (1,10)(2,9)(3,12,4,11)(5,13,6,14)(7,15)(8,16), (1,2)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
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 8, $C_4\times C_2$ x 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 12, $C_2^2:C_4$ x 16, $C_4\times C_2^2$ x 14, $C_2^4$ 32: $C_2^3 : C_4 $ x 8, $C_2^3 : D_4 $ x 4, $C_2 \times (C_2^2:C_4)$ x 12, $C_2^2 \times D_4$ x 2, 32T34 64: 16T68 x 2, 16T76 x 12, 16T87 x 4, 32T262 128: 32T992, 32T1107 x 2 256: 16T454 x 2, 16T470 512: 32T11559 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 8: $C_4\times C_2$
Low degree siblings
16T1090 x 16, 16T1099 x 8, 16T1102 x 7, 32T35333 x 16, 32T35334 x 32, 32T35335 x 8, 32T35336 x 16, 32T35337 x 32, 32T35338 x 16, 32T35339 x 8, 32T35410 x 8, 32T35411 x 32, 32T35412 x 8, 32T35413 x 8, 32T35414 x 4, 32T35415 x 4, 32T35439 x 16, 32T35440 x 16, 32T35441 x 4, 32T35442 x 64, 32T35443 x 16, 32T35444 x 16, 32T35445 x 16, 32T35446 x 16, 32T35447 x 8, 32T35448 x 16, 32T35449 x 4, 32T35450 x 8, 32T35451 x 16, 32T35452 x 8, 32T35453 x 16, 32T44298 x 4, 32T45936 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 64 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. |