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Properties

Label 46T42
46T42 1 21 1->21 46 1->46 2 16 2->16 40 2->40 3 20 3->20 42 3->42 4 17 4->17 39 4->39 5 18 5->18 36 5->36 6 15 6->15 37 6->37 7 19 7->19 29 7->29 8 13 8->13 28 8->28 9 22 9->22 24 9->24 10 10->8 30 10->30 11 11->7 31 11->31 12 12->11 38 12->38 13->2 34 13->34 14 14->3 43 14->43 15->5 27 15->27 23 16->23 45 16->45 17->6 44 17->44 18->10 33 18->33 19->14 35 19->35 20->12 25 20->25 21->4 41 21->41 32 22->32 23->1 26 23->26 24->1 24->45 25->14 25->46 26->21 26->32 27->23 27->43 28->4 28->34 29->6 29->26 30->20 30->35 31->8 31->28 32->15 32->31 33->17 33->29 34->3 34->33 35->9 35->37 36->2 36->42 37->13 37->27 38->40 39->22 40->18 40->41 41->11 41->36 42->10 42->25 43->7 43->24 44->19 45->30 46->5 46->38
Degree $46$
Order $2.081\times 10^{14}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $M_{23}\wr C_2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 42);
 

Group invariants

Abstract group:  $M_{23}\wr C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $208119169843200=2^{15} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \cdot 23^{2}$
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 $n$:  $46$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $42$
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:  $(1,46,5,36,2,40,18,33,17,44,19,35,9,24)(3,42,10,30,20,25,14,43,7,29,6,37,13,34)(4,39,22,32,15,27,23,26,21,41,11,31,8,28)(12,38)(16,45)$, $(1,21,4,17,6,15,5,18,10,8,13,2,16,23)(3,20,12,11,7,19,14)(9,22)(24,45,30,35,37,27,43)(25,46,38,40,41,36,42)(26,32,31,28,34,33,29)$
Copy content magma:Generators(G);
 

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: 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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed