Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1472$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,16,3,14)(2,15,4,13)(5,9,8,11)(6,10,7,12), (1,3)(2,4)(7,8)(9,10)(15,16), (1,11)(2,12)(3,9)(4,10)(5,13)(6,14)(7,16)(8,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 12, $C_2^3$ 16: $D_4\times C_2$ x 6, $Q_8:C_2$ 32: $C_2^2 \wr C_2$ x 3, 16T34 x 3, $C_4^2:C_2$ 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 6, 32T320 128: $C_2 \wr C_2\wr C_2$ x 4, 16T336 x 4, 16T350 x 3 256: 32T5721 x 4, 32T6030 512: 16T949, 16T964 x 2 1024: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1472 x 31, 32T99312 x 16, 32T99313 x 16, 32T99314 x 32, 32T99315 x 32, 32T99316 x 32, 32T99317 x 16, 32T99318 x 16, 32T99319 x 16, 32T99320 x 32, 32T99321 x 16, 32T99322 x 16, 32T110258 x 16, 32T116102 x 32Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 74 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. |