Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1643$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $8$ | |
| Generators: | (1,4,9,12)(2,3,10,11)(5,16,13,7,6,15,14,8), (1,3,10,11)(2,4,9,12)(5,15,13,7)(6,16,14,8), (1,4,6,8,9,11,14,16)(2,3,5,7,10,12,13,15) | |
| $|\Aut(F/K)|$: | $2$ |
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: $QD_{16}$ x 2, $D_4\times C_2$ x 3 32: $Z_8 : Z_8^\times$, $C_2^2 \wr C_2$, 16T48 64: $(((C_4 \times C_2): C_2):C_2):C_2$, 16T138, 16T155 128: $C_2 \wr C_2\wr C_2$ x 2, 32T1557 256: 16T700 512: 32T16861 1024: 16T1252 2048: 32T104606 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $QD_{16}$
Low degree siblings
16T1637 x 16, 16T1643 x 15, 32T208119 x 16, 32T208120 x 8, 32T208121 x 8, 32T208122 x 8, 32T208123 x 8, 32T208124 x 8, 32T208125 x 8, 32T208126 x 8, 32T208127 x 8, 32T208128 x 8, 32T208129 x 8, 32T208130 x 8, 32T208131 x 8, 32T208132 x 8, 32T208133 x 8, 32T208212 x 8, 32T208213 x 32, 32T208214 x 8, 32T208215 x 8, 32T208216 x 8, 32T208217 x 32, 32T208218 x 8, 32T208219 x 8, 32T208220 x 32, 32T208221 x 32, 32T208222 x 8, 32T208223 x 8, 32T208224 x 8, 32T208225 x 8, 32T208226 x 8, 32T208227 x 8, 32T208228 x 8, 32T208229 x 8, 32T221516 x 8, 32T221517 x 8, 32T224705 x 8, 32T249074 x 4, 32T249943 x 4, 32T313972 x 4, 32T314024 x 4, 32T327111 x 4, 32T396544 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 64 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. |