Group action invariants
| Degree $n$: | $34$ | |
| Transitive number $t$: | $13$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (2,14,17,5)(3,10,16,9)(4,6,15,13)(7,11,12,8)(18,25,19,29)(20,33,34,21)(22,24,32,30)(23,28,31,26), (1,26,7,21,13,33,2,28,8,23,14,18,3,30,9,25,15,20,4,32,10,27,16,22,5,34,11,29,17,24,6,19,12,31) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T15 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2312=2^{3} \cdot 17^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |