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Properties

Label 46T10
46T10 1 5 1->5 33 1->33 2 6 2->6 24 2->24 3 7 3->7 38 3->38 4 8 4->8 29 4->29 9 5->9 43 5->43 10 6->10 34 6->34 11 7->11 25 7->25 12 8->12 39 8->39 13 9->13 30 9->30 14 10->14 44 10->44 15 11->15 35 11->35 16 12->16 26 12->26 17 13->17 40 13->40 18 14->18 31 14->31 19 15->19 45 15->45 20 16->20 36 16->36 21 17->21 27 17->27 22 18->22 41 18->41 23 19->23 32 19->32 20->1 46 20->46 21->2 37 21->37 22->3 28 22->28 23->4 42 23->42 24->1 24->28 25->19 25->27 26->14 27->9 28->4 29->22 29->46 30->17 30->45 31->12 31->44 32->7 32->43 33->2 33->42 34->20 34->41 35->15 35->40 36->10 36->39 37->5 37->38 38->23 39->18 41->8 42->3 43->21 44->16 45->11 46->6
Degree $46$
Order $4232$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{23}\wr C_2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 10);
 

Group invariants

Abstract group:  $D_{23}\wr C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $4232=2^{3} \cdot 23^{2}$
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 $n$:  $46$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $10$
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:  $(1,5,9,13,17,21,2,6,10,14,18,22,3,7,11,15,19,23,4,8,12,16,20)(24,28)(25,27)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)$, $(1,33,2,24)(3,38,23,42)(4,29,22,28)(5,43,21,37)(6,34,20,46)(7,25,19,32)(8,39,18,41)(9,30,17,27)(10,44,16,36)(11,35,15,45)(12,26,14,31)(13,40)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T10

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

104 x 104 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed