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Properties

Label 38T16
38T16 1 9 1->9 27 1->27 2 17 2->17 31 2->31 3 6 3->6 35 3->35 4 14 4->14 20 4->20 5 5->3 24 5->24 11 6->11 28 6->28 7 19 7->19 32 7->32 8 36 8->36 16 9->16 21 9->21 10 10->5 25 10->25 13 11->13 29 11->29 12 12->2 33 12->33 13->10 37 13->37 18 14->18 22 14->22 15 15->7 26 15->26 16->15 30 16->30 17->4 34 17->34 18->12 38 18->38 19->1 23 19->23 20->15 20->31 21->1 21->24 22->6 22->36 23->11 23->29 24->16 24->22 25->2 25->34 26->7 26->27 27->12 27->20 28->17 28->32 29->3 29->25 30->8 30->37 31->13 31->30 32->18 32->23 33->4 33->35 34->9 34->28 35->14 35->21 36->19 36->33 37->5 37->26 38->10
Degree $38$
Order $4332$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{19}^2:D_6$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 16);
 

Group invariants

Abstract group:  $C_{19}^2:D_6$
Copy content magma:IdentifyGroup(G);
 
Order:  $4332=2^{2} \cdot 3 \cdot 19^{2}$
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 $t$:  $16$
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:  $(1,9,16,15,7,19)(2,17,4,14,18,12)(3,6,11,13,10,5)(20,31,30,37,26,27)(21,24,22,36,33,35)(23,29,25,34,28,32)$, $(1,27,12,33,4,20,15,26,7,32,18,38,10,25,2,31,13,37,5,24,16,30,8,36,19,23,11,29,3,35,14,22,6,28,17,34,9,21)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

There are no siblings 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

63 x 63 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed