Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $919$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (9,13)(10,14), (1,13,2,14)(3,11,4,12)(5,10,6,9)(7,16,8,15), (1,2)(3,4)(5,6)(7,8), (1,4)(2,3)(5,8)(6,7)(9,14)(10,13)(11,16)(12,15) | |
| $|\Aut(F/K)|$: | $4$ |
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: $C_2 \wr C_2\wr C_2$ x 4, 16T241, 16T245, 16T325 256: 16T509 x 2, 32T4223 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$ x 3
Degree 8: $C_2^2 \wr C_2$, $C_2 \wr C_2\wr C_2$ x 2
Low degree siblings
16T919 x 255, 32T10570 x 64, 32T10571 x 256, 32T10572 x 128, 32T10573 x 64, 32T10574 x 128, 32T10575 x 64, 32T10576 x 64, 32T10577 x 64, 32T10578 x 64, 32T10579 x 64, 32T17282 x 32, 32T17424 x 32Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $512=2^{9}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [512, 418967] |
| Character table: Data not available. |