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Properties

Label 44T1744
44T1744 1 22 1->22 36 1->36 2 21 2->21 35 2->35 3 23 3->23 33 3->33 4 24 4->24 34 4->34 5 7 5->7 27 5->27 6 8 6->8 28 6->28 7->6 26 7->26 8->5 25 8->25 9 9->7 9->28 10 10->8 10->27 11 11->6 11->25 12 12->5 12->26 13 20 13->20 30 13->30 14 19 14->19 29 14->29 15 17 15->17 31 15->31 16 18 16->18 32 16->32 17->31 41 17->41 18->32 42 18->42 19->29 44 19->44 20->30 43 20->43 21->12 21->15 22->11 22->16 23->9 23->14 24->10 24->13 25->4 38 25->38 26->3 37 26->37 27->1 39 27->39 28->2 40 28->40 29->21 29->39 30->22 30->40 31->24 31->38 32->23 32->37 33->12 33->34 34->11 35->10 35->36 36->9 37->2 37->13 38->1 38->14 39->4 39->15 40->3 40->16 41->18 41->42 42->17 43->19 43->44 44->20
Degree $44$
Order $33218887680$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^{21}.C_2.M_{11}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(44, 1744);
 

Group invariants

Abstract group:  $C_2^{21}.C_2.M_{11}$
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 $t$:  $1744$
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:  $(1,22,11,25,4,24,10,27)(2,21,12,26,3,23,9,28)(5,7,6,8)(13,20,30,40,16,18,32,37)(14,19,29,39,15,17,31,38)(33,34)(35,36)(41,42)(43,44)$, $(1,36,9,7,26,37,2,35,10,8,25,38)(3,33,12,5,27,39,4,34,11,6,28,40)(13,30,22,16,32,23,14,29,21,15,31,24)(17,41,18,42)(19,44,20,43)$
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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 11: $M_{11}$

Degree 22: 22T44

Low degree siblings

44T1732 x 2, 44T1744

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