Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1433$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,15,4,13,2,16,3,14)(5,6)(9,12)(10,11), (1,13,4,15,2,14,3,16)(5,9,7,11,6,10,8,12), (1,5,3,8)(2,6,4,7)(9,16,10,15)(11,14)(12,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 12, $C_2 \times (C_2^2:C_4)$ x 3 64: $((C_8 : C_2):C_2):C_2$ x 8, 16T76 x 6, 16T79 128: 16T227 x 4, 16T240 x 3 256: 16T502 x 2, 16T581 512: 16T911 1024: 32T61722 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1433 x 15, 32T98944 x 8, 32T98945 x 32, 32T98946 x 8, 32T98947 x 8, 32T98948 x 32, 32T98949 x 8, 32T98950 x 8, 32T98951 x 8, 32T98952 x 8, 32T107388 x 8, 32T107394 x 8, 32T142151 x 4, 32T182640 x 4, 32T182693 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 68 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. |