Properties

Label 34T15
34T15 1 24 1->24 26 1->26 2 21 2->21 29 2->29 3 18 3->18 32 3->32 4 4->18 4->32 5 5->21 5->29 6 6->24 6->26 7 23 7->23 27 7->27 8 20 8->20 30 8->30 9 33 9->33 34 9->34 10 19 10->19 31 10->31 11 22 11->22 28 11->28 12 25 12->25 12->25 13 13->22 13->28 14 14->19 14->31 15 15->33 15->34 16 16->20 16->30 17 17->23 17->27 18->5 18->13 19->7 19->16 20->1 20->10 21->4 21->12 22->6 22->15 23->9 24->3 24->11 25->5 25->14 26->8 26->16 27->2 27->10 28->4 28->13 29->7 29->15 30->1 30->9 31->3 31->12 32->6 32->14 33->8 33->17 34->2 34->11
Degree $34$
Order $2312$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{17}\wr C_2$

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Show commands: Magma

magma: G := TransitiveGroup(34, 15);
 

Group invariants

Abstract group:  $D_{17}\wr C_2$
magma: IdentifyGroup(G);
 
Order:  $2312=2^{3} \cdot 17^{2}$
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 $t$:  $15$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,24,3,18,5,29,7,23,9,34,11,28,13,22,15,33,17,27,2,21,4,32,6,26,8,20,10,31,12,25,14,19,16,30)$, $(1,26,16,20)(2,29,15,34)(3,32,14,31)(4,18,13,28)(5,21,12,25)(6,24,11,22)(7,27,10,19)(8,30,9,33)(17,23)$
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$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

34T13, 34T15

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

65 x 65 character table

magma: CharacterTable(G);
 

Regular extensions

Data not computed