Properties

Label 34T13
Order \(2312\)
n \(34\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $34$
Transitive number $t$ :  $13$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $1$

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 2

Siblings 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:  Data not available
Character table: Data not available.