Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1378$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,10,2,9)(3,11)(4,12)(5,13)(6,14)(7,15,8,16), (1,15,2,16)(3,5,4,6)(7,9)(8,10)(11,13)(12,14), (1,5)(2,6)(3,16,4,15)(7,11)(8,12)(9,13)(10,14), (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 14, 16T105 x 7 128: 16T241 x 7, 16T245 x 7, 16T325 256: 32T4223 x 7 512: 16T907 x 7 1024: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 7
Degree 4: $C_2^2$ x 7
Degree 8: $C_2^3$
Low degree siblings
16T1352 x 112, 16T1378 x 15, 32T98023 x 112, 32T98024 x 168, 32T98025 x 168, 32T98026 x 56, 32T98027 x 168, 32T98028 x 168, 32T98029 x 56, 32T98309 x 168, 32T98310 x 56, 32T98311 x 224, 32T98312 x 56, 32T98313 x 224, 32T98314 x 168, 32T98315 x 56, 32T98316 x 8, 32T105228 x 56Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 95 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. |