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Properties

Label 38T66
38T66 1 10 1->10 11 1->11 2 9 2->9 12 2->12 3 3->1 26 3->26 4 4->2 25 4->25 5 7 5->7 13 5->13 6 8 6->8 14 6->14 33 7->33 38 7->38 34 8->34 37 8->37 9->3 28 9->28 10->4 27 10->27 11->3 11->28 12->4 12->27 17 13->17 21 13->21 18 14->18 22 14->22 15 16 15->16 24 15->24 23 16->23 17->14 17->33 18->13 18->34 19 32 19->32 36 19->36 20 31 20->31 35 20->35 21->2 30 21->30 22->1 29 22->29 23->9 23->30 24->10 24->29 25->5 25->35 26->6 26->36 27->6 27->19 28->5 28->20 29->7 29->11 30->8 30->12 31->16 31->21 32->15 32->22 33->17 33->24 34->18 34->23 35->32 35->38 36->31 36->37 37->20 37->26 38->19 38->25
Degree $38$
Order $1.594\times 10^{22}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^{18}.A_{19}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(38, 66);
 

Group invariants

Abstract group:  $C_2^{18}.A_{19}$
Copy content magma:IdentifyGroup(G);
 
Order:  $15944266600786427904000=2^{33} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
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 $t$:  $66$
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:  $(1,10,4,25,35,38,19,32,15,24,29,11,28,5,7,33,17,14,22)(2,9,3,26,36,37,20,31,16,23,30,12,27,6,8,34,18,13,21)$, $(1,11,3)(2,12,4)(5,13,17,33,24,10,27,19,36,31,21,30,8,37,26,6,14,18,34,23,9,28,20,35,32,22,29,7,38,25)(15,16)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$60822550204416000$:  $A_{19}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $A_{19}$

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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed