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Properties

Label 36T6267
Degree $36$
Order $5184$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^6:C_3\wr C_3$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 6267);
 

Group invariants

Abstract group:  $C_2^6:C_3\wr C_3$
Copy content magma:IdentifyGroup(G);
 
Order:  $5184=2^{6} \cdot 3^{4}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $36$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $6267$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $3$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,13,18,30,23,27)(2,14,16,29,22,25)(3,15,17,28,24,26)(4,35,11,32,8,19)(5,36,10,33,7,21)(6,34,12,31,9,20)$, $(1,4,8,19,14,34,2,5,7,21,15,35,3,6,9,20,13,36)(10,24,26,28,31,16,12,23,27,30,32,17,11,22,25,29,33,18)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$3$:  $C_3$ x 4
$9$:  $C_3^2$
$27$:  $C_3^2:C_3$
$81$:  $C_3 \wr C_3 $
$1728$:  12T229

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $C_3$

Degree 4: None

Degree 6: None

Degree 9: $C_3 \wr C_3 $

Degree 12: 12T229

Degree 18: None

Low degree siblings

36T6267 x 2, 36T6268 x 6

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

Copy content magma:ConjugacyClasses(G);
 

Character table

56 x 56 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed