↑

Properties

Label 36T88318
Degree $36$
Order $559872000$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2\times A_6\wr S_3$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 88318);
 

Group invariants

Abstract group:  $C_2\times A_6\wr S_3$
Copy content magma:IdentifyGroup(G);
 
Order:  $559872000=2^{11} \cdot 3^{7} \cdot 5^{3}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
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 $t$:  $88318$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,9,4,6)(2,10,3,5)(7,11)(8,12)(13,28,16,31)(14,27,15,32)(17,36,23,25,19,30,22,33)(18,35,24,26,20,29,21,34)$, $(1,26,17,12,36,20,6,28,23,3,30,13,9,31,22,2,25,18,11,35,19,5,27,24,4,29,14,10,32,21)(7,34,15,8,33,16)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$279936000$:  18T971

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $D_{6}$

Degree 9: None

Degree 12: None

Degree 18: 18T971

Low degree siblings

36T88318 x 3

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