Group action invariants
| Degree $n$ : | $34$ | |
| Transitive number $t$ : | $10$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,8,15,5,12,2,9,16,6,13,3,10,17,7,14,4,11)(18,28,21,31,24,34,27,20,30,23,33,26,19,29,22,32,25), (1,25,14,23,10,21,6,19,2,34,15,32,11,30,7,28,3,26,16,24,12,22,8,20,4,18,17,33,13,31,9,29,5,27) | |
| $|\Aut(F/K)|$: | $17$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 17: $C_{17}$ 34: $D_{17}$, $C_{34}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T10 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 170 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $578=2 \cdot 17^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [578, 3] |
| Character table: Data not available. |