Properties

Label 13T9
Degree $13$
Order $6227020800$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{13}$

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Show commands: Magma

magma: G := TransitiveGroup(13, 9);
 

Group action invariants

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

Low degree resolvents

|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

There are 101 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $6227020800=2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  6227020800.a
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);