Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1638$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $8$ | |
| Generators: | (1,3,6,8,9,11,14,16,2,4,5,7,10,12,13,15), (9,10)(13,14)(15,16), (1,13)(2,14)(3,11)(4,12)(5,10,6,9) | |
| $|\Aut(F/K)|$: | $2$ |
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: 16T1253 2048: 16T1459 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $D_{8}$
Low degree siblings
16T1638 x 15, 16T1646 x 16, 32T208134 x 8, 32T208135 x 32, 32T208136 x 32, 32T208137 x 8, 32T208138 x 8, 32T208139 x 16, 32T208140 x 32, 32T208141 x 8, 32T208142 x 32, 32T208143 x 8, 32T208144 x 8, 32T208145 x 8, 32T208146 x 8, 32T208147 x 8, 32T208148 x 8, 32T208149 x 8, 32T208150 x 8, 32T208151 x 8, 32T208152 x 8, 32T208259 x 8, 32T208260 x 8, 32T208261 x 8, 32T208262 x 8, 32T208263 x 8, 32T208264 x 8, 32T208265 x 8, 32T208266 x 8, 32T208267 x 8, 32T208268 x 8, 32T208269 x 8, 32T208270 x 8, 32T208271 x 8, 32T208272 x 8, 32T212279 x 16, 32T212281 x 16, 32T221501 x 8, 32T221509 x 8, 32T224668 x 8, 32T248907 x 4, 32T249794 x 4, 32T313907 x 4, 32T314021 x 4, 32T326971 x 4, 32T396568 x 4Siblings 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. |