Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1744$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $7$ | |
| Generators: | (1,7,5,3)(2,8,6,4)(9,10)(11,16)(12,15)(13,14), (1,7,2,8)(3,6)(4,5)(9,11,13,15,10,12,14,16), (1,13,5,10)(2,14,6,9)(3,16,7,12)(4,15,8,11) | |
| $|\Aut(F/K)|$: | $2$ |
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 12, $C_2^3$ 16: $D_4\times C_2$ x 6, $Q_8:C_2$ 32: $C_2^2 \wr C_2$ x 3, 16T34 x 3, $C_4^2:C_2$ 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 6, 32T320 128: $C_2 \wr C_2\wr C_2$ x 4, 16T342 x 4, 16T350 x 3 256: 32T5807 x 4, 32T6030 512: 16T956, 16T969 x 2 1024: 32T41928 2048: 16T1439 4096: 32T316881 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_2 \wr C_2\wr C_2$
Low degree siblings
16T1739 x 8, 16T1744 x 7, 32T400429 x 4, 32T400430 x 4, 32T400431 x 4, 32T400432 x 4, 32T400433 x 4, 32T400434 x 4, 32T400435 x 4, 32T400436 x 8, 32T400437 x 4, 32T400438 x 4, 32T400439 x 4, 32T400440 x 4, 32T400441 x 4, 32T400442 x 4, 32T400443 x 4, 32T400502 x 4, 32T400503 x 4, 32T400504 x 4, 32T400505 x 4, 32T400506 x 4, 32T400507 x 4, 32T400508 x 4, 32T400509 x 4, 32T400510 x 4, 32T400511 x 4, 32T400512 x 4, 32T400513 x 4, 32T400514 x 4, 32T400515 x 4, 32T406504 x 4, 32T406506 x 4, 32T408439 x 4, 32T408457 x 4, 32T430876 x 2, 32T430883 x 2, 32T430902 x 2, 32T430952 x 2, 32T430978 x 2, 32T431049 x 2, 32T548452 x 2, 32T548480 x 2, 32T549312 x 2, 32T549339 x 2, 32T549461 x 2, 32T549626 x 2, 32T549655 x 2, 32T549668 x 2, 32T644663 x 2, 32T644697 x 2, 32T665927 x 2, 32T665932 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 95 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. |