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Properties

Label 38T49
38T49 1 17 1->17 32 1->32 2 18 2->18 31 2->31 3 19 3->19 34 3->34 4 20 4->20 33 4->33 5 22 5->22 36 5->36 6 21 6->21 35 6->35 7 24 7->24 37 7->37 8 23 8->23 38 8->38 9 9->1 26 9->26 10 10->2 25 10->25 11 11->4 28 11->28 12 12->3 27 12->27 13 13->5 29 13->29 14 14->6 30 14->30 15 15->7 15->31 16 16->8 16->32 17->10 17->34 18->9 18->33 19->11 19->36 20->12 20->35 21->13 21->38 22->14 22->37 23->2 23->15 24->1 24->16 25->3 25->18 26->4 26->17 27->6 27->19 28->5 28->20 29->7 29->22 30->8 30->21 31->10 31->23 32->9 32->24 33->12 33->25 34->11 34->26 35->13 35->28 36->14 36->27 37->15 37->30 38->16 38->29
Degree $38$
Order $9961472$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{18}.C_{38}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 49);
 

Group invariants

Abstract group:  $C_2^{18}.C_{38}$
Copy content magma:IdentifyGroup(G);
 
Order:  $9961472=2^{19} \cdot 19$
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 $t$:  $49$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,32,24,16,8,38,29,22,14,6,35,28,20,12,3,34,26,17,10,2,31,23,15,7,37,30,21,13,5,36,27,19,11,4,33,25,18,9)$, $(1,17,34,11,28,5,22,37,15,31,10,25,3,19,36,14,30,8,23,2,18,33,12,27,6,21,38,16,32,9,26,4,20,35,13,29,7,24)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$19$:  $C_{19}$
$38$:  $C_{38}$
$4980736$:  38T48

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $C_{19}$

Low degree siblings

38T49 x 13796

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