Properties

Label 22T48
Degree $22$
Order $125452800$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $M_{11}\wr C_2$

Related objects

Downloads

Learn more

Show commands: Magma

magma: G := TransitiveGroup(22, 48);
 

Group action invariants

Degree $n$:  $22$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $48$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $M_{11}\wr C_2$
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:  (1,16,2,14,11,17,8,18,6,15,9,20)(3,22,10,19)(4,21,7,13,5,12), (1,16,6,19,9,20,11,17,5,14,8,22,4,13,3,12)(2,18)(7,15,10,21)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

24T24600, 44T1454

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 65 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $125452800=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  125452800.a
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);