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Properties

Label 36T103805
Degree $36$
Order $4586471424$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{18}.C_3^3.C_3^3.S_4$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 103805);
 

Group invariants

Abstract group:  $C_2^{18}.C_3^3.C_3^3.S_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $4586471424=2^{21} \cdot 3^{7}$
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 $t$:  $103805$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,25,19,8,21,11,33,32,14,4,26,18,6,24,12,36,30,16,3,27,17,7,22,10,35,29,13)(2,28,20,5,23,9,34,31,15)$, $(1,20,34,9,5,16,4,17,33,11,7,15,2,18,36,10,8,13)(3,19,35,12,6,14)(21,23,24)(25,27,28)(29,31,32)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$24$:  $S_4$
$648$:  $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
$17496$:  27T912

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: None

Degree 6: None

Degree 9: $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$

Degree 12: None

Degree 18: None

Low degree siblings

36T103805 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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed