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Properties

Label 34T13
34T13 1 26 1->26 2 14 2->14 28 2->28 3 10 3->10 30 3->30 4 6 4->6 32 4->32 5 5->2 34 5->34 15 6->15 19 6->19 7 11 7->11 21 7->21 8 8->7 23 8->23 9 9->3 25 9->25 16 10->16 27 10->27 12 11->12 29 11->29 12->8 31 12->31 13 13->4 33 13->33 17 14->17 18 14->18 15->13 20 15->20 16->9 22 16->22 17->5 24 17->24 18->3 18->25 19->12 19->29 20->4 20->33 21->13 21->20 22->5 22->24 23->14 23->28 24->6 24->32 25->15 25->19 26->7 26->23 27->16 28->8 28->31 29->17 29->18 30->9 30->22 31->1 31->26 32->10 32->30 33->2 33->34 34->11 34->21
Degree 3434
Order 23122312
Cyclic no
Abelian no
Solvable yes
Primitive no
pp-group no
Group: D17≀C2D_{17}\wr C_2

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Copy content magma:G := TransitiveGroup(34, 13);
 

Group invariants

Abstract group:  D17≀C2D_{17}\wr C_2
Copy content magma:IdentifyGroup(G);
 
Order:  2312=23⋅1722312=2^{3} \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 nn:  3434
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number tt:  1313
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  −1-1
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
#Aut⁡(F/K)\card{\Aut(F/K)}:  11
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (2,14,17,5)(3,10,16,9)(4,6,15,13)(7,11,12,8)(18,25,19,29)(20,33,34,21)(22,24,32,30)(23,28,31,26)(2,14,17,5)(3,10,16,9)(4,6,15,13)(7,11,12,8)(18,25,19,29)(20,33,34,21)(22,24,32,30)(23,28,31,26), (1,26,7,21,13,33,2,28,8,23,14,18,3,30,9,25,15,20,4,32,10,27,16,22,5,34,11,29,17,24,6,19,12,31)(1,26,7,21,13,33,2,28,8,23,14,18,3,30,9,25,15,20,4,32,10,27,16,22,5,34,11,29,17,24,6,19,12,31)
Copy content magma:Generators(G);
 

Low degree resolvents

#(G/N)\card{(G/N)}Galois groups for stem field(s)
22:  C2C_2 x 3
44:  C22C_2^2
88:  D4D_{4}

Resolvents shown for degrees ≤47\leq 47

Subfields

Degree 2: C2C_2

Degree 17: None

Low degree siblings

34T15 x 2

Siblings are shown with degree ≤47\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

65 x 65 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed