Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $860$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,6)(2,5)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15), (1,8,2,7)(3,6,4,5)(9,12,10,11)(13,15,14,16), (1,10,3,15)(2,9,4,16)(5,11,7,14)(6,12,8,13), (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: $C_2^2$ 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: $C_2$ x 3
Degree 4: $C_2^2$, $D_{4}$ x 2
Degree 8: $D_4$
Low degree siblings
16T819 x 8, 16T843 x 8, 16T850 x 4, 16T860 x 3, 16T879 x 8, 32T9894 x 8, 32T9895 x 8, 32T9896 x 8, 32T9897 x 16, 32T9898 x 8, 32T9899 x 4, 32T9900 x 8, 32T9901 x 4, 32T9902 x 8, 32T10114 x 8, 32T10115 x 8, 32T10116 x 4, 32T10117 x 4, 32T10118 x 8, 32T10159 x 4, 32T10160 x 8, 32T10161 x 2, 32T10162 x 4, 32T10163 x 4, 32T10164 x 2, 32T10165 x 4, 32T10235 x 4, 32T10236 x 2, 32T10237 x 4, 32T10238 x 4, 32T10239 x 2, 32T10240 x 4, 32T10241 x 8, 32T10242 x 4, 32T10243 x 4, 32T10244 x 8, 32T10245 x 4, 32T10246 x 4, 32T10247 x 8, 32T10348 x 8, 32T10349 x 4, 32T10350 x 8, 32T10351 x 4, 32T10352 x 4, 32T10353 x 4, 32T10354 x 8, 32T10355 x 4, 32T10356 x 4, 32T19764 x 2, 32T20043 x 2Siblings 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, 418986] |
| Character table: Data not available. |