Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1606$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $7$ | |
| Generators: | (1,14,5,10,2,13,6,9)(3,8,15,11,4,7,16,12), (1,5)(2,6)(3,15,4,16)(7,8)(11,12)(13,14), (1,5)(2,6)(3,15)(4,16)(7,14,12,10,8,13,11,9) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_4\wr C_2$ x 2, $C_2^2 \wr C_2$ x 4, $C_2 \times (C_2^2:C_4)$ x 3 64: $(C_4^2 : C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, 16T79, 16T106, 16T111, 16T138, 16T146 128: 32T1151, 32T1153, 32T1154 256: 16T482 x 2, 16T500 512: 32T13142 1024: 16T1141 2048: 32T134366 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_4\wr C_2$
Low degree siblings
16T1575 x 4, 16T1606 x 3, 32T207273 x 2, 32T207274 x 2, 32T207275 x 4, 32T207276 x 2, 32T207277 x 2, 32T207278 x 2, 32T207279 x 2, 32T207751 x 4, 32T207752 x 4, 32T207753 x 4, 32T207754 x 4, 32T207755 x 2, 32T207756 x 2, 32T207757 x 2, 32T207758 x 2, 32T207759 x 2, 32T207760 x 2, 32T220250 x 2, 32T220251 x 2, 32T250313 x 2, 32T250354, 32T250362, 32T250375, 32T250383, 32T327162, 32T327167, 32T327811, 32T327815 x 2, 32T327824, 32T327846, 32T327869, 32T377711 x 2, 32T389723, 32T389724Siblings 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. |