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Properties

Label 36T119057
Degree $36$
Order $705277476864$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^{12}.C_2^8.C_3^4.D_4:D_4$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 119057);
 

Group invariants

Abstract group:  $C_3^{12}.C_2^8.C_3^4.D_4:D_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $705277476864=2^{14} \cdot 3^{16}$
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 $t$:  $119057$
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:  $(1,32,15,20,27,9,2,33,14,21,26,7,3,31,13,19,25,8)(4,36,30,11,16,22)(5,34,28,12,17,23)(6,35,29,10,18,24)$, $(1,5,26,17,2,6,25,16,3,4,27,18)(7,10,32,23,8,12,31,24)(9,11,33,22)(13,28,14,30,15,29)(19,36,21,34)(20,35)$, $(1,36,8,29,27,22,32,16,3,34,7,30,26,23,33,18)(2,35,9,28,25,24,31,17)(4,13,12,19)(5,14,11,20,6,15,10,21)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$8$:  $D_{4}$ x 6, $C_2^3$
$16$:  $D_4\times C_2$ x 3
$32$:  $C_2^2 \wr C_2$
$64$:  $(C_4^2 : C_2):C_2$
$5184$:  12T266
$1327104$:  16T1934

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 4: $D_{4}$

Degree 6: None

Degree 9: None

Degree 12: 12T266

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