Properties

Label 33T39
Degree $33$
Order $31944$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^3:S_4$

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Show commands: Magma

magma: G := TransitiveGroup(33, 39);
 

Group action invariants

Degree $n$:  $33$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $39$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{11}^3:S_4$
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:  (1,19,25,3,22,24,5,14,23,7,17,33,9,20,32,11,12,31,2,15,30,4,18,29,6,21,28,8,13,27,10,16,26), (1,30,11,24)(2,25,10,29)(3,31,9,23)(4,26,8,28)(5,32,7,33)(6,27)(12,17,22,16,21,15,20,14,19,13,18)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$24$:  $S_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

44T230

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 100 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $31944=2^{3} \cdot 3 \cdot 11^{3}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  31944.v
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);