↑

Properties

Label 46T23
46T23 1 10 1->10 32 1->32 2 20 2->20 34 2->34 3 7 3->7 36 3->36 4 17 4->17 38 4->38 5 5->4 40 5->40 6 14 6->14 42 6->42 7->1 44 7->44 8 11 8->11 46 8->46 9 21 9->21 25 9->25 10->8 27 10->27 18 11->18 29 11->29 12 12->5 31 12->31 13 15 13->15 33 13->33 14->2 35 14->35 15->12 37 15->37 16 22 16->22 39 16->39 17->9 41 17->41 19 18->19 43 18->43 19->6 45 19->45 20->16 24 20->24 21->3 26 21->26 22->13 28 22->28 23 30 23->30 24->22 24->33 25->17 25->31 26->12 26->29 27->7 28->2 28->25 29->20 29->46 30->15 30->44 31->10 31->42 32->5 32->40 33->23 33->38 34->18 34->36 35->13 35->34 36->8 36->32 37->3 37->30 38->21 38->28 39->26 40->11 40->24 41->6 41->45 42->1 42->43 43->19 43->41 44->14 44->39 45->9 45->37 46->4 46->35
Degree $46$
Order $256036$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{23}^2:(C_{11}\times D_{22})$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 23);
 

Group invariants

Abstract group:  $C_{23}^2:(C_{11}\times D_{22})$
Copy content magma:IdentifyGroup(G);
 
Order:  $256036=2^{2} \cdot 11^{2} \cdot 23^{2}$
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 $t$:  $23$
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:  $(1,32,5,40,11,29,20,24,22,28,2,34,18,43,19,45,9,25,17,41,6,42)(3,36,8,46,4,38,21,26,12,31,10,27,7,44,14,35,13,33,23,30,15,37)(16,39)$, $(1,10,8,11,18,19,6,14,2,20,16,22,13,15,12,5,4,17,9,21,3,7)(24,33,38,28,25,31,42,43,41,45,37,30,44,39,26,29,46,35,34,36,32,40)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1 x 3
$44$:  $D_{22}$, 44T2
$242$:  22T7
$484$:  44T27

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