Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1477$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,13,4,16,2,14,3,15)(5,10,8,11,6,9,7,12), (1,11,3,9,2,12,4,10)(7,8)(15,16), (1,4,2,3)(5,7,6,8)(9,12,10,11)(13,14)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
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: $(C_4^2 : C_2):C_2$ x 2, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 32T320 128: $C_2 \wr C_2\wr C_2$ x 2, 16T336, 16T342, 16T350, 16T382, 16T408 256: 32T5721, 32T5807, 32T6155 512: 16T997, 16T998, 16T1025 1024: 32T42529 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
16T1477 x 15, 32T99350 x 8, 32T99351 x 8, 32T99352 x 8, 32T99353 x 8, 32T99354 x 8, 32T99355 x 8, 32T99356 x 8, 32T122194 x 8, 32T144392 x 8, 32T145161 x 4Siblings 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. |