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Properties

Label 22T47
22T47 1 13 1->13 15 1->15 2 14 2->14 16 2->16 3 3->15 17 3->17 4 4->16 18 4->18 5 5->1 19 5->19 6 6->2 20 6->20 7 7->4 7->5 8 8->3 8->6 9 9->7 12 9->12 10 10->8 11 10->11 11->2 11->6 12->1 12->5 13->3 13->20 14->4 14->19 15->9 15->10 16->9 16->10 17->8 22 17->22 18->7 21 18->21 19->11 19->21 20->12 20->22 21->14 21->17 22->13 22->18
Degree $22$
Order $79833600$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2\times S_{11}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 47);
 

Group invariants

Abstract group:  $C_2\times S_{11}$
Copy content magma:IdentifyGroup(G);
 
Order:  $79833600=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
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 $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $47$
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:  $(1,13,20,22,18,7,4,16,10,11,6,2,14,19,21,17,8,3,15,9,12,5)$, $(1,15,10,8,6,20,12)(2,16,9,7,5,19,11)(3,17,22,13)(4,18,21,14)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$39916800$:  $S_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $S_{11}$

Low degree siblings

22T47, 44T1258

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

112 x 112 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed