↑

Properties

Label 38T36
38T36 1 2 1->2 21 1->21 29 2->29 3 19 3->19 37 3->37 4 18 4->18 26 4->26 5 17 5->17 34 5->34 6 16 6->16 23 6->23 7 15 7->15 31 7->31 8 14 8->14 20 8->20 9 13 9->13 28 9->28 10 12 10->12 36 10->36 11 25 11->25 33 12->33 22 13->22 30 14->30 38 15->38 27 16->27 35 17->35 24 18->24 32 19->32 20->14 20->25 21->26 22->7 22->27 23->13 23->28 24->19 24->29 25->6 25->30 26->12 26->31 27->18 27->32 28->5 28->33 29->11 29->34 30->17 30->35 31->4 31->36 32->10 32->37 33->16 33->38 34->3 34->20 35->9 35->21 36->15 36->22 37->2 37->23 38->8 38->24
Degree $38$
Order $25992$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{19}^2:C_{18}$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 36);
 

Group invariants

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

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$3$:  $C_3$
$4$:  $C_2^2$
$6$:  $C_6$ x 3
$8$:  $D_{4}$
$9$:  $C_9$
$12$:  $C_6\times C_2$
$18$:  $C_{18}$ x 3
$24$:  $D_4 \times C_3$
$36$:  36T2
$72$:  36T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T36

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

53 x 53 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed