Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1701$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,2)(7,8), (1,10)(2,9)(3,12,4,11)(5,13,6,14)(7,15)(8,16), (7,12,8,11)(9,14,10,13), (1,2)(3,16)(4,15)(7,10,11,14,8,9,12,13), (1,15)(2,16)(3,6,4,5)(7,12)(8,11)(9,14,10,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 42, $C_2^4$ 32: $C_2^2 \wr C_2$ x 28, $C_2^2 \times D_4$ x 7 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 14, 16T105 x 7 128: 16T241 x 7, 16T245 x 7, 16T325 256: 32T4223 x 7 512: 16T907 x 7 1024: 64T? 2048: 16T1352 4096: 32T314244 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1701 x 15, 32T399613 x 8, 32T399614 x 8, 32T399615 x 8, 32T399616 x 8, 32T399617 x 8, 32T399618 x 8, 32T399619 x 8, 32T399620 x 8, 32T399621 x 8, 32T399622 x 8, 32T399623 x 8, 32T399624 x 8, 32T399625 x 8, 32T399626 x 8, 32T399627 x 8, 32T405329 x 8, 32T405334 x 8, 32T421949 x 4, 32T421955 x 4, 32T422007 x 4, 32T545771 x 4, 32T545774 x 4, 32T644649 x 4, 32T644691 x 4, 32T665910 x 4, 32T665924 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 119 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8192=2^{13}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |