Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1430$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,16,10,6,2,15,9,5)(3,14,11,8,4,13,12,7), (1,11,4,10,2,12,3,9)(5,6)(13,14), (1,15,11,7,3,14,10,6,2,16,12,8,4,13,9,5) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 8, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 4, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 2, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$, $C_2^3 : C_4 $ x 4, $C_4 \times D_4$ x 2, $C_2 \times (C_2^2:C_4)$, 16T34 x 2, 16T37 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T76 x 2, 32T239 128: $C_2 \wr C_2\wr C_2$ x 2, 16T208, 16T218, 16T230, 16T345 x 2 256: 32T3729, 32T4357 x 2 512: 16T893 1024: 32T58414 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_2 \wr C_2\wr C_2$
Low degree siblings
16T1430 x 7, 32T98916 x 4, 32T98917 x 4, 32T98918 x 4, 32T98919 x 4, 32T98920 x 4, 32T98921 x 4, 32T98922 x 4, 32T116188 x 4, 32T144384 x 2, 32T144387 x 2, 32T144388 x 2, 32T144612 x 4, 32T144621 x 4, 32T145171 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 71 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2048=2^{11}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |