Group action invariants
| Degree $n$ : | $34$ | |
| Transitive number $t$ : | $29$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,9,13,18,21,25,29,33,3,7,11,15,19,23,28,32)(2,6,10,14,17,22,26,30,34,4,8,12,16,20,24,27,31), (1,32,28,23,19,15,11,8,4,33,29,25,22,17,14,9,5,2,31,27,24,20,16,12,7,3,34,30,26,21,18,13,10,6) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 17: $C_{17}$ 34: $C_{34}$ 4352: 34T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 17: $C_{17}$
Low degree siblings
34T29 x 14Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 64 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8704=2^{9} \cdot 17$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |