Properties

Label 39T21
Degree $39$
Order $507$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{13}:C_{39}$

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Show commands: Magma

magma: G := TransitiveGroup(39, 21);
 

Group action invariants

Degree $n$:  $39$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $21$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{13}:C_{39}$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $13$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,28,22,11,35,20,9,31,24,2,38,19,13,39,25,10,37,23,12,33,16,7,32,18,4,30,21,5,34,15,8,36,14,3,29,26,6,27,17), (1,21,27,8,23,34,7,24,33,13,17,38,11,15,28,3,16,36,4,19,32,10,22,39,9,14,35,6,18,29,5,25,30,12,20,37,2,26,31)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$13$:  $C_{13}$
$39$:  $C_{13}:C_3$, $C_{39}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T21 x 3

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 91 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $507=3 \cdot 13^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  507.3
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);