Group action invariants
| Degree $n$ : | $34$ | |
| Transitive number $t$ : | $45$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,8,28,13,34,19,5,25,12,32,18,3,24,10,29,16,2,22,7,27,14,33,20,6,26,11,31,17,4,23,9,30,15), (1,31)(2,32)(3,29)(4,30)(5,27,6,28)(7,25)(8,26)(9,23)(10,24)(11,22)(12,21)(13,20,14,19)(15,17,16,18)(33,34) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 34: $D_{17}$ 68: $D_{34}$ 8704: 34T30 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 17: $D_{17}$
Low degree siblings
34T45 x 29Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 80 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $17408=2^{10} \cdot 17$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |