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Properties

Label 36T19593
Degree $36$
Order $93312$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_6^4.\SOPlus(4,2)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 19593);
 

Group invariants

Abstract group:  $C_6^4.\SOPlus(4,2)$
Copy content magma:IdentifyGroup(G);
 
Order:  $93312=2^{7} \cdot 3^{6}$
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 $t$:  $19593$
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:  $(1,32,15,19,9,29,3,36,18,23,8,25,5,33,13,21,11,28)(2,31,16,20,10,30,4,35,17,24,7,26,6,34,14,22,12,27)$, $(1,12,3,10,5,7)(2,11,4,9,6,8)(13,14)(15,16)(17,18)(19,26,35,20,25,36)(21,27,31,24,29,33)(22,28,32,23,30,34)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$8$:  $D_{4}$
$12$:  $D_{6}$
$24$:  $(C_6\times C_2):C_2$
$72$:  $C_3^2:D_4$
$216$:  12T116, 18T105
$648$:  18T215
$1152$:  $S_4\wr C_2$
$3456$:  24T7222, 36T4431
$5832$:  18T505
$10368$:  36T8546

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 4: None

Degree 6: $C_3^2:D_4$

Degree 9: None

Degree 12: 12T202

Degree 18: 18T505

Low degree siblings

36T19592 x 3, 36T19593 x 2, 36T19594 x 3, 36T19595 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

107 x 107 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed