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Properties

Label 21T51
21T51 1 13 1->13 14 1->14 2 15 2->15 2->15 3 3->13 3->14 4 12 4->12 17 4->17 5 11 5->11 18 5->18 6 10 6->10 16 6->16 7 8 7->8 19 7->19 21 8->21 9 20 9->20 10->1 10->5 11->2 11->4 12->3 12->6 13->2 13->5 14->1 14->6 15->3 15->4 16->9 16->19 17->7 17->20 18->8 18->21 19->11 20->10 21->12
Degree $21$
Order $10206$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_3^6:D_7$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(21, 51);
 

Group invariants

Abstract group:  $C_3^6:D_7$
Copy content magma:IdentifyGroup(G);
 
Order:  $10206=2 \cdot 3^{6} \cdot 7$
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 $n$:  $21$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $51$
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:  $(1,14,6,16,9,20,10)(2,15,4,17,7,19,11)(3,13,5,18,8,21,12)$, $(1,13,2,15,3,14)(4,12,6,10,5,11)(7,8)(16,19)(17,20)(18,21)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$14$:  $D_{7}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $D_{7}$

Low degree siblings

21T51 x 12, 21T52 x 13, 42T555 x 13, 42T556 x 13, 42T557 x 13

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

96 x 96 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed