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Properties

Label 36T90487
Degree $36$
Order $816293376$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^{12}.C_4^2.S_4.C_2^2$

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Copy content magma:G := TransitiveGroup(36, 90487);
 

Group invariants

Abstract group:  $C_3^{12}.C_4^2.S_4.C_2^2$
Copy content magma:IdentifyGroup(G);
 
Order:  $816293376=2^{9} \cdot 3^{13}$
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 $t$:  $90487$
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:  $(1,27,3,25)(2,26)(4,10,6,12,5,11)(7,32,8,33)(9,31)(13,34,15,36)(14,35)(16,24,18,22)(17,23)(19,28,21,29,20,30)$, $(1,13,29,2,14,30)(3,15,28)(4,18,35,6,17,34,5,16,36)(7,10,25,8,12,26)(9,11,27)(19,24,32,21,23,33,20,22,31)$, $(1,29,3,30,2,28)(4,24,5,22,6,23)(7,9,8)(10,27,12,26,11,25)(13,14,15)(16,20,17,19,18,21)(31,36,33,35,32,34)$
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
$6$:  $S_3$
$8$:  $C_2^3$
$12$:  $D_{6}$ x 3
$24$:  $S_4$ x 3, $S_3 \times C_2^2$
$48$:  $S_4\times C_2$ x 9
$96$:  $V_4^2:S_3$, 12T48 x 3
$192$:  12T100 x 3
$384$:  12T139
$768$:  16T1063
$1536$:  24T3330

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: $S_4$

Degree 6: $S_4$

Degree 9: None

Degree 12: $S_4$

Degree 18: None

Low degree siblings

36T90640, 36T91436, 36T91901

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