Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1719$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,10,2,9)(3,11)(4,12)(5,13)(6,14)(7,15,8,16), (1,15,2,16)(3,5,4,6)(7,9)(8,10)(11,13)(12,14), (3,4)(7,9)(8,10)(11,13)(12,14)(15,16), (1,2)(3,4)(5,6)(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 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 6, 16T105 x 7 128: $C_2 \wr C_2\wr C_2$ x 12, 16T241 x 3, 16T245 x 3, 16T325 256: 16T509 x 6, 32T4223 x 3 512: 16T819 x 3, 16T907, 16T919 x 3 1024: 32T40151 x 3 2048: 16T1340 4096: 32T317640 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$ x 3
Degree 8: $C_2^2 \wr C_2$
Low degree siblings
16T1719 x 15, 16T1728 x 48, 32T399975 x 48, 32T399976 x 24, 32T399977 x 48, 32T399978 x 48, 32T399979 x 24, 32T399980 x 24, 32T399981 x 24, 32T399982 x 24, 32T399983 x 24, 32T399984 x 24, 32T399985 x 24, 32T399986 x 24, 32T399987 x 24, 32T399988 x 48, 32T399989 x 48, 32T399990 x 24, 32T399991 x 8, 32T399992 x 8, 32T399993 x 8, 32T400215 x 24, 32T400216 x 48, 32T400217 x 24, 32T400218 x 24, 32T400219 x 24, 32T400220 x 48, 32T400221 x 48, 32T400222 x 24, 32T400223 x 24, 32T400224 x 24, 32T400225 x 48, 32T400226 x 24, 32T400227 x 48, 32T400228 x 24, 32T400229 x 24, 32T400230 x 24, 32T400231 x 48, 32T400232 x 24, 32T400233 x 48, 32T400234 x 24, 32T400235 x 24, 32T400236 x 48, 32T405528 x 8, 32T431383 x 12, 32T431523 x 12, 32T431732 x 24, 32T431871 x 24, 32T519524 x 24, 32T522319 x 12, 32T549500 x 12, 32T549570 x 12, 32T640154 x 24, 32T715889 x 12Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 152 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. |