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Properties

Label 13T9
13T9 1 2 1->2 1->2 3 2->3 4 3->4 5 4->5 6 5->6 7 6->7 8 7->8 9 8->9 10 9->10 11 10->11 12 11->12 13 12->13 13->1
Degree $13$
Order $6227020800$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{13}$

Related objects

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Show commands: Magma

Copy content magma:G := TransitiveGroup(13, 9);
 

Group invariants

Abstract group:  $S_{13}$
Copy content magma:IdentifyGroup(G);
 
Order:  $6227020800=2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $13$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
CHM label:   $S13$
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  yes
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,2,3,4,5,6,7,8,9,10,11,12,13)$, $(1,2)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

26T83

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

101 x 101 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed