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Properties

Label 36T33409
Degree $36$
Order $663552$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9.C_3^4:\OD_{16}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(36, 33409);
 

Group invariants

Abstract group:  $C_2^9.C_3^4:\OD_{16}$
Copy content magma:IdentifyGroup(G);
 
Order:  $663552=2^{13} \cdot 3^{4}$
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 $t$:  $33409$
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:  $(1,11,15,17,2,12,16,18)(3,10,13,7)(4,9,14,8)(19,33,28,31,20,34,27,32)(21,35,25,24)(22,36,26,23)(29,30)$, $(1,30,6,33,17,36,14,19)(2,29,5,34,18,35,13,20)(3,24)(4,23)(7,27,15,31,11,26,10,22)(8,28,16,32,12,25,9,21)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $D_{4}$ x 2, $C_8$ x 2, $C_4\times C_2$
$16$:  $C_8:C_2$, $C_2^2:C_4$, $C_8\times C_2$
$32$:  $C_2^2 : C_8$
$1296$:  12T215
$2592$:  24T5244
$331776$:  16T1907

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: None

Degree 4: None

Degree 6: None

Degree 9: None

Degree 12: None

Degree 18: 18T288

Low degree siblings

24T20616 x 2, 24T20619 x 2, 32T2439261 x 2, 32T2439262 x 2, 36T33409 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