Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1398$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,5,3,7)(2,6,4,8)(9,13,12,16)(10,14,11,15), (1,3,2,4)(5,7,6,8)(9,11,10,12)(13,14)(15,16), (1,12,4,10,2,11,3,9)(5,13,8,16,6,14,7,15) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2^2 \wr C_2$, $C_2^3 : C_4 $ x 4, $C_4 \times D_4$ 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, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T76 x 2, 32T239 128: 16T208, 16T218, 16T230, 16T234 x 2, 16T235 x 2 256: 32T3729, 32T4050 x 2 512: 16T847 x 2, 16T938 1024: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1398 x 31, 32T98547 x 16, 32T98548 x 16, 32T98549 x 32, 32T98550 x 32, 32T98551 x 16, 32T98552 x 16, 32T98553 x 32, 32T98554 x 16, 32T98555 x 32, 32T98556 x 16, 32T98557 x 16, 32T110322 x 16, 32T115726 x 32Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 71 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. |