Properties

Label 34T10
Order \(578\)
n \(34\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
17:  $C_{17}$
34:  $D_{17}$, $C_{34}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T10 x 7

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 170 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $578=2 \cdot 17^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [578, 3]
Character table: Data not available.