Properties

Label 34T10
Degree $34$
Order $578$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{17}\times D_{17}$

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Show commands: Magma

magma: G := TransitiveGroup(34, 10);
 

Group invariants

Abstract group:  $C_{17}\times D_{17}$
magma: IdentifyGroup(G);
 
Order:  $578=2 \cdot 17^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
magma: NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $34$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $10$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $17$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,8,15,5,12,2,9,16,6,13,3,10,17,7,14,4,11)(18,28,21,31,24,34,27,20,30,23,33,26,19,29,22,32,25)$, $(1,25,14,23,10,21,6,19,2,34,15,32,11,30,7,28,3,26,16,24,12,22,8,20,4,18,17,33,13,31,9,29,5,27)$
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$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

Conjugacy classes not computed

magma: ConjugacyClasses(G);
 

Character table

Character table not computed

magma: CharacterTable(G);
 

Regular extensions

Data not computed