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Properties

Label 44T1731
44T1731 1 5 1->5 35 1->35 2 6 2->6 36 2->36 3 7 3->7 34 3->34 4 8 4->8 33 4->33 12 5->12 20 5->20 11 6->11 19 6->19 9 7->9 18 7->18 10 8->10 17 8->17 31 9->31 38 9->38 32 10->32 37 10->37 29 11->29 39 11->39 30 12->30 40 12->40 13 13->7 15 13->15 14 14->8 16 14->16 15->6 15->14 16->5 16->13 17->20 21 17->21 18->19 22 18->22 23 19->23 24 20->24 21->4 43 21->43 22->3 44 22->44 23->1 41 23->41 24->2 42 24->42 25 25->12 25->16 26 26->11 26->15 27 27->9 27->13 28 28->10 28->14 29->2 29->33 30->1 30->34 31->3 31->36 32->4 32->35 33->26 33->28 34->25 34->27 35->25 35->28 36->26 36->27 37->32 37->40 38->31 38->39 39->30 40->29 41->21 42->22 43->23 44->24
Degree $44$
Order $33218887680$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^{22}.M_{11}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(44, 1731);
 

Group invariants

Abstract group:  $C_2^{22}.M_{11}$
Copy content magma:IdentifyGroup(G);
 
Order:  $33218887680=2^{26} \cdot 3^{2} \cdot 5 \cdot 11$
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 $n$:  $44$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1731$
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:  $(1,5,20,24,2,6,19,23)(3,7,18,22)(4,8,17,21)(9,31,36,27)(10,32,35,28)(11,29,33,26)(12,30,34,25)(13,15,14,16)(37,40)(38,39)$, $(1,35,25,16,5,12,40,29,2,36,26,15,6,11,39,30)(3,34,27,13,7,9,38,31)(4,33,28,14,8,10,37,32)(17,20)(18,19)(21,43,23,41)(22,44,24,42)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$7920$:  $M_{11}$
$15840$:  22T26
$8110080$:  22T43
$16220160$:  22T44, 24T24094 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 11: $M_{11}$

Degree 22: $M_{11}$

Low degree siblings

44T1731, 44T1742 x 2

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