Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1340$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,5)(2,6)(3,7)(4,8)(9,16)(10,15)(11,13)(12,14), (9,10)(11,12)(13,14)(15,16), (1,4)(2,3)(5,7)(6,8)(9,12)(10,11)(13,15)(14,16), (1,3)(2,4), (1,12,2,11)(3,9,4,10) | |
| $|\Aut(F/K)|$: | $4$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_2 \wr C_2\wr C_2$ x 3
Low degree siblings
16T1340 x 511, 32T97863 x 128, 32T97864 x 768, 32T97865 x 768, 32T97866 x 384, 32T97867 x 384, 32T97868 x 384, 32T97869 x 384, 32T97870 x 384, 32T97871 x 384, 32T112187 x 192, 32T112231 x 64, 32T112277 x 192, 32T113099 x 192, 32T113154 x 384, 32T114069 x 64, 32T114426 x 192Siblings 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. |