Group action invariants
| Degree $n$: | $34$ | |
| Transitive number $t$: | $15$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,24,3,18,5,29,7,23,9,34,11,28,13,22,15,33,17,27,2,21,4,32,6,26,8,20,10,31,12,25,14,19,16,30), (1,26,16,20)(2,29,15,34)(3,32,14,31)(4,18,13,28)(5,21,12,25)(6,24,11,22)(7,27,10,19)(8,30,9,33)(17,23) |
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
34T13, 34T15Siblings 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. |