Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1354$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (7,8)(9,11,10,12)(15,16), (1,12)(2,11)(3,9)(4,10)(5,13)(6,14)(7,15)(8,16), (1,13,11,6,3,16,10,7,2,14,12,5,4,15,9,8) | |
| $|\Aut(F/K)|$: | $2$ |
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: $((C_8 : C_2):C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T76 x 2, 32T239 128: 16T208, 16T218, 16T219 x 2, 16T227 x 2, 16T230 256: 32T3729, 32T4019 x 2 512: 16T912 1024: 32T63476 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 8: $((C_8 : C_2):C_2):C_2$
Low degree siblings
16T1354 x 15, 32T98041 x 8, 32T98042 x 16, 32T98043 x 16, 32T98044 x 16, 32T98045 x 8, 32T98046 x 8, 32T98047 x 16, 32T98048 x 8, 32T98049 x 8, 32T98050 x 8, 32T98051 x 8, 32T110365 x 8, 32T141675 x 4, 32T182445 x 4, 32T182576 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 59 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. |