Properties

Label 46T13
Degree $46$
Order $23276$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{23}^2:D_{22}$

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Show commands: Magma

magma: G := TransitiveGroup(46, 13);
 

Group action invariants

Degree $n$:  $46$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $13$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{23}^2:D_{22}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,39,5,26,9,36,13,46,17,33,21,43,2,30,6,40,10,27,14,37,18,24,22,34,3,44,7,31,11,41,15,28,19,38,23,25,4,35,8,45,12,32,16,42,20,29), (1,23,12,6,9,19,14,5,21,13,17,15,16,4,10,7,20,2,11,18,3,22)(24,40,31,26,36,39,33,45,44,46,42,27,34,43,25,38,35,41,29,30,28,32)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$22$:  $D_{11}$
$44$:  $D_{22}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 59 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $23276=2^{2} \cdot 11 \cdot 23^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  23276.a
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);