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Properties

Label 34T11
34T11 1 4 1->4 32 1->32 2 3 2->3 23 2->23 31 3->31 22 4->22 5 17 5->17 30 5->30 6 16 6->16 21 6->21 7 15 7->15 29 7->29 8 14 8->14 20 8->20 9 13 9->13 28 9->28 10 12 10->12 19 10->19 11 27 11->27 18 12->18 26 13->26 34 14->34 25 15->25 33 16->33 24 17->24 18->17 18->23 19->15 19->22 20->13 20->21 21->11 22->9 23->7 24->5 24->34 25->3 25->33 26->1 26->32 27->16 27->31 28->14 28->30 29->12 30->10 31->8 32->6 33->4 34->2
Degree $34$
Order $1156$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{17}^2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(34, 11);
 

Group invariants

Abstract group:  $D_{17}^2$
Copy content magma:IdentifyGroup(G);
 
Order:  $1156=2^{2} \cdot 17^{2}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$34$:  $D_{17}$ x 2
$68$:  $D_{34}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T11 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

Copy content magma:ConjugacyClasses(G);
 

Character table

100 x 100 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed