Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1432$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,10)(2,9)(3,11)(4,12)(5,6)(7,8)(13,16,14,15), (1,3,2,4)(5,7,6,8)(9,10)(11,12)(13,16,14,15), (1,14,4,16,2,13,3,15)(5,12,6,11)(7,10,8,9) | |
| $|\Aut(F/K)|$: | $4$ |
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: 16T871, 16T876, 16T890 1024: 32T40794 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
16T1432 x 15, 32T98937 x 8, 32T98938 x 8, 32T98939 x 8, 32T98940 x 8, 32T98941 x 8, 32T98942 x 8, 32T98943 x 8, 32T116199 x 8, 32T144391 x 4, 32T144443 x 4, 32T145174 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: | $2048=2^{11}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |