Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1642$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $8$ | |
| Generators: | (1,16)(2,15)(3,14)(4,13)(5,6)(9,12,10,11), (1,3,2,4)(5,7,6,8)(9,12,10,11), (1,10,2,9)(3,12,4,11)(5,15)(6,16)(7,14)(8,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 6, $C_2^3$ 16: $D_{8}$ x 2, $D_4\times C_2$ x 3 32: $Z_8 : Z_8^\times$, $C_2^2 \wr C_2$, 16T29 64: $(C_4^2 : C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, 16T126 128: $C_2 \wr C_2\wr C_2$ x 2, 16T409 256: 16T689 512: 16T962 1024: 16T1271 2048: 16T1446 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
16T1642 x 31, 32T208197 x 16, 32T208198 x 16, 32T208199 x 16, 32T208200 x 16, 32T208201 x 16, 32T208202 x 16, 32T208203 x 16, 32T208204 x 16, 32T208205 x 16, 32T208206 x 16, 32T208207 x 16, 32T208208 x 16, 32T208209 x 16, 32T208210 x 16, 32T208211 x 16, 32T224368 x 16, 32T249758 x 8, 32T313919 x 8, 32T314047 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 73 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. |