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Properties

Label 38T35
38T35 1 21 1->21 32 1->32 2 29 2->29 38 2->38 3 26 3->26 36 3->36 4 23 4->23 34 4->34 5 20 5->20 5->32 6 30 6->30 6->36 7 28 7->28 33 7->33 8 8->26 8->30 9 24 9->24 27 9->27 10 22 10->22 10->24 11 11->20 11->21 12 37 12->37 12->37 13 13->34 35 13->35 14 31 14->31 14->33 15 15->28 15->31 16 25 16->25 16->29 17 17->22 17->27 18 18->25 18->38 19 19->23 19->35 20->3 20->17 21->2 21->13 22->4 22->6 23->10 23->14 24->5 24->14 25->15 26->3 26->6 27->7 27->16 28->7 28->11 29->15 29->17 30->19 31->4 31->18 32->8 32->9 33->12 33->19 34->10 34->16 35->1 35->1 36->5 36->11 37->2 37->9 38->12 38->13
Degree $38$
Order $25992$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{19}^2:(C_3\times S_3)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 35);
 

Group invariants

Abstract group:  $D_{19}^2:(C_3\times S_3)$
Copy content magma:IdentifyGroup(G);
 
Order:  $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$
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 $t$:  $35$
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:  $(1,21,2,38,13,35)(3,36,5,32,8,26)(4,34,16,29,15,31)(6,30,19,23,10,22)(7,28,11,20,17,27)(9,24,14,33,12,37)(18,25)$, $(1,32,9,27,16,25,15,28,7,33,19,35)(2,29,17,22,4,23,14,31,18,38,12,37)(3,26,6,36,11,21,13,34,10,24,5,20)(8,30)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$3$:  $C_3$
$4$:  $C_2^2$
$6$:  $S_3$, $C_6$ x 3
$8$:  $D_{4}$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$
$24$:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
$36$:  $C_6\times S_3$
$72$:  12T42

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

54 x 54 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed