Properties

Label 34T12
34T12 1 22 1->22 31 1->31 2 25 2->25 34 2->34 3 20 3->20 28 3->28 4 23 4->23 4->31 5 26 5->26 5->34 6 6->20 29 6->29 7 7->23 32 7->32 8 18 8->18 8->26 9 21 9->21 9->29 10 24 10->24 10->32 11 11->18 27 11->27 12 12->21 30 12->30 13 13->24 33 13->33 14 19 14->19 14->27 15 15->22 15->30 16 16->25 16->33 17 17->19 17->28 18->4 19->2 19->15 20->9 20->13 21->3 21->7 22->1 22->14 23->8 23->12 24->2 24->6 25->13 25->17 26->7 26->11 27->1 27->5 28->12 28->16 29->6 29->10 30->4 30->17 31->11 31->15 32->5 32->9 33->3 34->10 34->14
Degree $34$
Order $1156$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{17}^2:C_4$

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Show commands: Magma

magma: G := TransitiveGroup(34, 12);
 

Group invariants

Abstract group:  $C_{17}^2:C_4$
magma: IdentifyGroup(G);
 
Order:  $1156=2^{2} \cdot 17^{2}$
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 $t$:  $12$
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:  $(1,31,15,22)(2,34,14,19)(3,20,13,33)(4,23,12,30)(5,26,11,27)(6,29,10,24)(7,32,9,21)(8,18)(16,25,17,28)$, $(1,22,14,27)(2,25,13,24)(3,28,12,21)(4,31,11,18)(5,34,10,32)(6,20,9,29)(7,23,8,26)(15,30,17,19)(16,33)$
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$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 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

76 x 76 character table

magma: CharacterTable(G);
 

Regular extensions

Data not computed