Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $868$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (9,10)(11,12)(13,14)(15,16), (3,4)(7,8)(11,12)(15,16), (1,4,2,3)(5,7,6,8), (1,9)(2,10)(3,12)(4,11)(5,15,6,16)(7,13,8,14), (1,8,2,7)(3,6,4,5)(9,10)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $D_{4}$ x 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 42, $C_2^4$ 32: $C_2^2 \wr C_2$ x 28, $C_2^2 \times D_4$ x 7 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T105 x 7 128: 16T241, 16T245, 16T325 256: 32T4223 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$ x 3
Degree 8: $C_2^2 \wr C_2$
Low degree siblings
16T868 x 23, 32T10287 x 12, 32T10288 x 24, 32T10289 x 24, 32T10290 x 24, 32T10291 x 24, 32T10292 x 12, 32T10293 x 24, 32T10294 x 12, 32T10295 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 53 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $512=2^{9}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [512, 419034] |
| Character table: Data not available. |