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Properties

Label 46T21
46T21 1 29 1->29 40 1->40 2 27 2->27 39 2->39 3 26 3->26 37 3->37 4 24 4->24 36 4->36 5 34 5->34 46 5->46 6 33 6->33 44 6->44 7 31 7->31 43 7->43 8 30 8->30 41 8->41 9 28 9->28 9->40 10 10->27 38 10->38 11 25 11->25 11->37 12 12->24 35 12->35 13 13->34 45 13->45 14 32 14->32 14->44 15 15->31 42 15->42 16 16->29 16->41 17 17->28 17->39 18 18->26 18->38 19 19->25 19->36 20 20->35 20->46 21 21->33 21->45 22 22->32 22->43 23 23->30 23->42 24->13 24->20 25->5 25->19 26->20 27->12 27->17 28->4 28->16 29->15 29->19 30->11 30->14 31->3 31->13 32->12 32->18 33->10 33->11 34->2 34->10 35->9 35->17 36->8 36->9 37->1 37->7 38->6 38->16 39->5 39->8 40->4 40->23 41->3 41->15 42->2 42->7 43->1 43->22 44->23 45->6 45->22 46->21 46->21
Degree $46$
Order $128018$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{23}^2:(C_{11}\times D_{11})$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 21);
 

Group invariants

Abstract group:  $C_{23}^2:(C_{11}\times D_{11})$
Copy content magma:IdentifyGroup(G);
 
Order:  $128018=2 \cdot 11^{2} \cdot 23^{2}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  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 $t$:  $21$
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:  $(1,40,4,24,20,46,21,33,11,25,19,36,8,41,3,37,7,31,13,45,22,43)(2,27,17,39,5,34,10,38,6,44,23,30,14,32,12,35,9,28,16,29,15,42)(18,26)$, $(1,29,19,25,5,46,21,45,6,33,10,27,12,24,13,34,2,39,8,30,11,37)(3,26,20,35,17,28,4,36,9,40,23,42,7,43,22,32,18,38,16,41,15,31)(14,44)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1
$242$:  22T7

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

104 x 104 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed