Group action invariants
| Degree $n$ : | $34$ | |
| Transitive number $t$ : | $12$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,31,15,22)(2,34,14,19)(3,20,13,33)(4,23,12,30)(5,26,11,27)(6,29,10,24)(7,32,9,21)(8,18)(16,25,17,28), (1,22,14,27)(2,25,13,24)(3,28,12,21)(4,31,11,18)(5,34,10,32)(6,20,9,29)(7,23,8,26)(15,30,17,19)(16,33) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 68: $C_{17}:C_{4}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 17: None
Low degree siblings
34T12 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 76 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1156=2^{2} \cdot 17^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1156, 11] |
| Character table: Data not available. |