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Properties

Label 36T89207
Degree $36$
Order $594542592$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^{16}.\SL(2,8).(C_3\times S_3)$

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Copy content magma:G := TransitiveGroup(36, 89207);
 

Group invariants

Abstract group:  $C_2^{16}.\SL(2,8).(C_3\times S_3)$
Copy content magma:IdentifyGroup(G);
 
Order:  $594542592=2^{20} \cdot 3^{4} \cdot 7$
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 $t$:  $89207$
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:  $(1,20,27,14,11,35,22,32,8,4,19,25,15,12,33,23,31,6)(2,18,26,13,9,34,21,30,5,3,17,28,16,10,36,24,29,7)$, $(1,23,16,33,29,28,9,4,24,13,34,32,27,12,3,21,14,35,31,26,11,2,22,15,36,30,25,10)(5,6,7,8)(17,19)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$18$:  $S_3\times C_3$
$1512$:  $\mathrm{P}\Gamma\mathrm{L}(2,8)$
$3024$:  18T427
$9072$:  27T797

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 4: None

Degree 6: None

Degree 9: $\mathrm{P}\Gamma\mathrm{L}(2,8)$

Degree 12: None

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