Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1429$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (9,10)(11,12), (1,16)(2,15)(3,10)(4,9)(5,11)(6,12)(7,14)(8,13), (1,8,6,3)(2,7,5,4)(11,12)(15,16) | |
| $|\Aut(F/K)|$: | $2$ |
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 8, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 4, $C_2^2:C_4$ x 4, $Q_8:C_2$ x 2, $C_4\times C_2^2$ 32: $C_4\wr C_2$ x 4, $C_2^2 \wr C_2$, $C_4 \times D_4$ x 2, $C_2 \times (C_2^2:C_4)$, 16T34 x 2, 16T37 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T111 x 2, 32T239 128: $C_2 \wr C_2\wr C_2$ x 2, 16T208, 16T211, 16T222, 16T345 x 2 256: 32T3766, 32T4357 x 2 512: 16T876 1024: 32T58388 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
16T1361 x 8, 16T1425 x 4, 16T1429 x 3, 32T98112 x 8, 32T98113 x 4, 32T98114 x 4, 32T98115 x 4, 32T98116 x 4, 32T98117 x 4, 32T98118 x 4, 32T98863 x 4, 32T98864 x 4, 32T98865 x 4, 32T98866 x 4, 32T98867 x 2, 32T98868 x 4, 32T98869 x 2, 32T98870 x 4, 32T98909 x 4, 32T98910 x 4, 32T98911 x 2, 32T98912 x 8, 32T98913 x 4, 32T98914 x 2, 32T98915 x 4, 32T140784 x 2, 32T140792 x 2, 32T140801 x 2, 32T144411 x 2, 32T144413 x 4, 32T144416 x 2, 32T144470 x 2, 32T144543 x 2, 32T144579 x 2, 32T144588 x 4, 32T144611 x 2, 32T144636 x 2, 32T145206 x 2, 32T180119 x 2, 32T192293 x 2, 32T192305 x 2, 32T192312 x 2, 32T192505 x 2, 32T202620 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 77 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2048=2^{11}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |