Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1769$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,2)(3,4)(5,14,6,13), (1,15,2,16)(3,5,4,6)(7,9)(8,10)(11,13)(12,14), (1,5)(2,6)(3,16,4,15)(7,11)(8,12)(9,13)(10,14), (15,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $D_{4}$ x 36, $C_2^3$ x 15 16: $D_4\times C_2$ x 54, $C_2^4$ 32: $C_2^2 \wr C_2$ x 24, $C_2^3 : D_4 $ x 6, $C_2^2 \times D_4$ x 9 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 24, 16T87 x 9, 16T98 x 2, 16T105 x 6, 16T109 x 18 128: 16T245 x 12, 32T1237 x 9, 32T1241 x 6 256: 16T531 x 18, 64T? 512: 32T13330 x 3 1024: 16T1152 2048: 32T183793 4096: 16T1591 x 3 8192: 128T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1769 x 127, 32T723622 x 192, 32T723623 x 192, 32T723624 x 192, 32T723625 x 192, 32T723626 x 64, 32T723627 x 64, 32T723628 x 192, 32T723629 x 64, 32T723630 x 192, 32T723631 x 192, 32T723632 x 192, 32T723633 x 64, 32T723634 x 384, 32T723635 x 192, 32T723636 x 192, 32T723637 x 384, 32T723638 x 192, 32T723639 x 384, 32T723640 x 384, 32T723641 x 192, 32T723642 x 384, 32T723643 x 192, 32T723644 x 192, 32T723645 x 384, 32T723646 x 192, 32T723647 x 384, 32T723648 x 384, 32T723649 x 192, 32T723650 x 192, 32T723651 x 192, 32T723652 x 192, 32T723653 x 192, 32T723654 x 192, 32T723655 x 192, 32T723656 x 192, 32T723657 x 192, 32T723658 x 64, 32T723659 x 64, 32T723660 x 64, 32T727332 x 192Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 220 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $16384=2^{14}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |