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Properties

Label 26T13
Degree $26$
Order $676$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{13}^2$

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Show commands: Magma

magma: G := TransitiveGroup(26, 13);
 

Group invariants

Abstract group:  $D_{13}^2$
magma: IdentifyGroup(G);
 
Order:  $676=2^{2} \cdot 13^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
magma: NilpotencyClass(G);
 

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$26$:  $D_{13}$ x 2
$52$:  $D_{26}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

26T13 x 5

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

magma: ConjugacyClasses(G);
 

Character table

64 x 64 character table

magma: CharacterTable(G);
 

Regular extensions

Data not computed