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Properties

Label 45T4982
Degree $45$
Order $860934420$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^{15}.(C_5\times A_4)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(45, 4982);
 

Group invariants

Abstract group:  $C_3^{15}.(C_5\times A_4)$
Copy content magma:IdentifyGroup(G);
 
Order:  $860934420=2^{2} \cdot 3^{16} \cdot 5$
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 $n$:  $45$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $4982$
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:  $(1,11,20,30,37,3,12,21,28,39,2,10,19,29,38)(4,15,23,32,41)(5,14,24,31,42,6,13,22,33,40)(7,18,25,36,45)(8,17,27,34,44,9,16,26,35,43)$, $(1,31,16)(2,32,17)(3,33,18)(4,36,19,6,34,20,5,35,21)(7,38,24,8,39,22,9,37,23)(10,41,26)(11,40,27)(12,42,25)(13,45,30)(14,44,29)(15,43,28)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$3$:  $C_3$
$5$:  $C_5$
$12$:  $A_4$
$15$:  $C_{15}$
$60$:  20T14
$324$:  $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$
$1620$:  45T188
$31886460$:  45T3107

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 5: $C_5$

Degree 9: None

Degree 15: $C_{15}$

Low degree siblings

45T4982 x 15

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