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Properties

Label 34T29
34T29 1 5 1->5 32 1->32 2 6 2->6 31 2->31 3 7 3->7 34 3->34 4 8 4->8 33 4->33 5->2 9 5->9 6->1 10 6->10 7->3 11 7->11 8->4 12 8->12 9->5 13 9->13 10->6 14 10->14 11->8 15 11->15 12->7 16 12->16 13->10 18 13->18 14->9 17 14->17 15->11 19 15->19 16->12 20 16->20 17->14 22 17->22 18->13 21 18->21 19->15 23 19->23 20->16 24 20->24 21->18 25 21->25 22->17 26 22->26 23->19 28 23->28 24->20 27 24->27 25->22 29 25->29 26->21 30 26->30 27->24 27->31 28->23 28->32 29->25 29->33 30->26 30->34 31->2 31->27 32->1 32->28 33->3 33->29 34->4 34->30
Degree $34$
Order $8704$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9:C_{17}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(34, 29);
 

Group invariants

Abstract group:  $C_2^9:C_{17}$
Copy content magma:IdentifyGroup(G);
 
Order:  $8704=2^{9} \cdot 17$
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 $t$:  $29$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,5,9,13,18,21,25,29,33,3,7,11,15,19,23,28,32)(2,6,10,14,17,22,26,30,34,4,8,12,16,20,24,27,31)$, $(1,32,28,23,19,15,11,8,4,33,29,25,22,17,14,9,5,2,31,27,24,20,16,12,7,3,34,30,26,21,18,13,10,6)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$17$:  $C_{17}$
$34$:  $C_{34}$
$4352$:  34T18

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 17: $C_{17}$

Low degree siblings

34T29 x 14

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

64 x 64 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed