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Properties

Label 15T25
15T25 1 6 1->6 2 7 2->7 3 3->6 8 3->8 4 9 4->9 5 10 5->10 6->9 11 6->11 12 7->12 13 8->13 9->12 14 9->14 15 10->15 11->1 12->2 12->15 13->3 14->4 15->3 15->5
Degree $15$
Order $375$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5\wr C_3$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(15, 25);
 

Group invariants

Abstract group:  $C_5\wr C_3$
Copy content magma:IdentifyGroup(G);
 
Order:  $375=3 \cdot 5^{3}$
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 $n$:  $15$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $25$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
CHM label:   $[5^{3}]3=5wr3$
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $5$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15)$, $(3,6,9,12,15)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$3$:  $C_3$
$5$:  $C_5$
$15$:  $C_{15}$
$75$:  $C_5^2 : C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 5: None

Low degree siblings

15T25 x 7

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

55 x 55 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed