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Properties

Label 38T12
38T12 1 12 1->12 25 1->25 2 11 2->11 21 2->21 3 10 3->10 36 3->36 4 9 4->9 32 4->32 5 8 5->8 28 5->28 6 7 6->7 24 6->24 20 7->20 35 8->35 31 9->31 27 10->27 23 11->23 38 12->38 13 19 13->19 34 13->34 14 18 14->18 30 14->30 15 17 15->17 26 15->26 16 22 16->22 37 17->37 33 18->33 29 19->29 20->17 20->33 21->3 21->32 22->8 22->31 23->13 23->30 24->18 24->29 25->4 25->28 26->9 26->27 27->14 28->19 29->5 30->10 31->15 32->1 33->6 34->11 34->38 35->16 35->37 36->2 37->7
Degree $38$
Order $1444$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{19}^2:C_4$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 12);
 

Group invariants

Abstract group:  $C_{19}^2:C_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $1444=2^{2} \cdot 19^{2}$
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 $t$:  $12$
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:  $(1,12)(2,11)(3,10)(4,9)(5,8)(6,7)(13,19)(14,18)(15,17)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(34,38)(35,37)$, $(1,25,4,32)(2,21,3,36)(5,28,19,29)(6,24,18,33)(7,20,17,37)(8,35,16,22)(9,31,15,26)(10,27,14,30)(11,23,13,34)(12,38)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T12 x 9

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

94 x 94 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed