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Properties

Label 46T44
46T44 1 5 1->5 29 1->29 2 6 2->6 30 2->30 3 17 3->17 39 3->39 4 18 4->18 40 4->40 12 5->12 26 5->26 11 6->11 25 6->25 7 7->4 14 7->14 8 8->3 13 8->13 9 9->39 44 9->44 10 10->40 43 10->43 20 11->20 32 11->32 19 12->19 31 12->31 16 13->16 24 13->24 15 14->15 23 14->23 15->20 15->32 16->19 16->31 17->25 17->29 18->26 18->30 27 19->27 34 19->34 28 20->28 33 20->33 21 21->23 45 21->45 22 22->24 46 22->46 35 23->35 38 23->38 36 24->36 37 24->37 25->15 25->27 26->16 26->28 27->6 27->9 28->5 28->10 29->8 29->18 30->7 30->17 31->1 41 31->41 32->2 42 32->42 33->37 34->38 35->2 35->46 36->1 36->45 37->11 37->21 38->12 38->22 39->13 40->14 41->35 41->43 42->36 42->44 43->21 44->22 45->8 45->42 46->7 46->41
Degree $46$
Order $2.585\times 10^{22}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $S_{23}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 44);
 

Group invariants

Abstract group:  $S_{23}$
Copy content magma:IdentifyGroup(G);
 
Order:  $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
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 $t$:  $44$
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:  $(1,5,26,28,10,40,14,15,32,2,6,25,27,9,39,13,16,31)(3,17,29,8)(4,18,30,7)(11,20,33,37)(12,19,34,38)(21,23,35,46,41,43)(22,24,36,45,42,44)$, $(1,29,18,26,16,19,27,6,11,32,42,36)(2,30,17,25,15,20,28,5,12,31,41,35)(3,39)(4,40)(7,14,23,38,22,46)(8,13,24,37,21,45)(9,44)(10,43)$
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: $S_{23}$

Low degree siblings

23T7

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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed