↑

Properties

Label 36T115877
Degree $36$
Order $88159684608$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^{12}.C_2^8.C_3^4.C_8$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 115877);
 

Group invariants

Abstract group:  $C_3^{12}.C_2^8.C_3^4.C_8$
Copy content magma:IdentifyGroup(G);
 
Order:  $88159684608=2^{11} \cdot 3^{16}$
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 $t$:  $115877$
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:  $(1,6,32,23,25,17,8,36,3,4,33,24,26,18,7,34,2,5,31,22,27,16,9,35)(10,13,30,19,11,15,29,20,12,14,28,21)$, $(1,4,8,34,25,18,21,11)(2,5,7,35,26,17,19,10)(3,6,9,36,27,16,20,12)(13,28,32,23,14,29,33,22,15,30,31,24)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$8$:  $C_8$
$72$:  $C_3^2:C_8$ x 2
$648$:  12T173
$165888$:  16T1894

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 4: $C_4$

Degree 6: None

Degree 9: None

Degree 12: 12T173

Degree 18: 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

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