Group action invariants
| Degree $n$ : | $34$ | |
| Transitive number $t$ : | $16$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,31,9,24)(2,28,8,27)(3,25,7,30)(4,22,6,33)(5,19)(10,21,17,34)(11,18,16,20)(12,32,15,23)(13,29,14,26), (1,32,12,28,6,24,17,20,11,33,5,29,16,25,10,21,4,34,15,30,9,26,3,22,14,18,8,31,2,27,13,23,7,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 68: $C_{17}:C_{4}$ x 2 136: 34T5 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T16 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $2312=2^{3} \cdot 17^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |