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Properties

Label 40T315648
40T315648 1 2 1->2 27 1->27 28 2->28 3 7 3->7 3->28 4 8 4->8 4->27 5 13 5->13 16 5->16 6 14 6->14 15 6->15 7->8 7->13 8->14 9 24 9->24 25 9->25 10 23 10->23 26 10->26 11 11->3 11->23 12 12->4 12->24 31 13->31 36 13->36 32 14->32 35 14->35 15->12 15->32 16->11 16->31 17 17->6 34 17->34 18 18->5 33 18->33 19 20 19->20 19->26 20->25 21 21->1 21->10 22 22->2 22->9 23->22 23->36 24->21 24->35 25->6 25->18 26->5 26->17 38 27->38 40 27->40 37 28->37 39 28->39 29 29->3 29->12 30 30->4 30->11 31->15 31->29 32->16 32->30 33->19 33->29 34->20 34->30 35->34 35->38 36->33 36->37 37->17 37->40 38->18 38->39 39->9 39->22 40->10 40->21
Degree $40$
Order $2.433\times 10^{18}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2.A_{20}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 315648);
 

Group invariants

Abstract group:  $C_2.A_{20}$
Copy content magma:IdentifyGroup(G);
 
Order:  $2432902008176640000=2^{18} \cdot 3^{8} \cdot 5^{4} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$
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 $n$:  $40$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $315648$
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:  $(1,27,38,39,9,24,21)(2,28,37,40,10,23,22)(3,7,13,36,33,19,26,17,6,15,32,30,11)(4,8,14,35,34,20,25,18,5,16,31,29,12)$, $(1,2)(3,28,39,22,9,25,6,14,32,16,11,23,36,37,17,34,30,4,27,40,21,10,26,5,13,31,15,12,24,35,38,18,33,29)(7,8)(19,20)$
Copy content magma:Generators(G);
 

Low degree resolvents

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

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: None

Degree 8: None

Degree 10: None

Degree 20: 20T1116

Low degree siblings

There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

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