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Properties

Label 38T14
38T14 1 11 1->11 21 1->21 2 12 2->12 23 2->23 3 13 3->13 25 3->25 4 14 4->14 27 4->27 5 15 5->15 29 5->29 6 16 6->16 31 6->31 7 17 7->17 33 7->33 8 18 8->18 35 8->35 9 19 9->19 37 9->37 10 10->1 20 10->20 11->2 22 11->22 12->3 24 12->24 13->4 26 13->26 14->5 28 14->28 15->6 30 15->30 16->7 32 16->32 17->8 34 17->34 18->9 36 18->36 19->10 38 19->38 20->19 20->27 21->15 21->28 22->29 23->7 23->30 24->3 24->31 25->18 25->32 26->14 26->33 27->10 27->34 28->6 28->35 29->2 29->36 30->17 30->37 31->13 31->38 32->9 32->20 33->5 33->21 34->1 34->22 35->16 35->23 36->12 36->24 37->8 37->25 38->4 38->26
Degree $38$
Order $2166$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 14);
 

Group invariants

Abstract group:  2166.7
Copy content magma:IdentifyGroup(G);
 
Order:  $2166=2 \cdot 3 \cdot 19^{2}$
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 $n$:  $38$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $14$
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:  $(1,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,10)(20,27,34,22,29,36,24,31,38,26,33,21,28,35,23,30,37,25,32)$, $(1,21,15,30,17,34)(2,23,7,33,5,29)(3,25,18,36,12,24)(4,27,10,20,19,38)(6,31,13,26,14,28)(8,35,16,32,9,37)(11,22)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$57$:  $C_{19}:C_{3}$
$114$:  $C_{19}:C_{6}$, 38T4

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T14 x 8

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