Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1547$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (3,4)(5,6)(7,10)(8,9)(11,14,12,13)(15,16), (3,5)(4,6)(7,8)(9,10)(11,13,12,14)(15,16), (1,2)(3,4), (1,10)(2,9)(3,12,4,11)(5,13,6,14)(7,15)(8,16), (1,6)(2,5)(3,16)(4,15)(7,12)(8,11)(9,14)(10,13), (1,16,2,15)(3,5,4,6)(9,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 63 4: $C_2^2$ x 651 8: $C_2^3$ x 1395 16: $C_2^4$ x 651 32: $C_2^3 : D_4 $ x 28, 32T39 x 63 64: 16T69 x 42, 64T? 128: 32T1011 x 7 256: 16T448 x 7 512: 64T? 1024: 16T1082 x 3 2048: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $C_2^3 : D_4 $
Low degree siblings
16T1547 x 31, 32T206833 x 48, 32T206834 x 48, 32T206835 x 48, 32T206836 x 96, 32T206837 x 96, 32T206838 x 16, 32T206839 x 48, 32T206840 x 48, 32T206841 x 48, 32T212711 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 133 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4096=2^{12}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |