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Properties

Label 22T31
22T31 1 6 1->6 17 1->17 2 10 2->10 16 2->16 3 15 3->15 4 7 4->7 14 4->14 5 11 5->11 13 5->13 6->4 12 6->12 8 7->8 22 7->22 8->1 21 8->21 9 9->5 20 9->20 10->9 19 10->19 11->2 18 11->18 12->7 12->21 13->6 13->12 14->5 15->4 15->16 16->3 16->18 17->2 17->20 18->1 18->22 19->11 19->13 20->10 20->15 21->9 21->17 22->8 22->19
Degree $22$
Order $24200$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $F_{11}\wr C_2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 31);
 

Group invariants

Abstract group:  $F_{11}\wr C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $24200=2^{3} \cdot 5^{2} \cdot 11^{2}$
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 $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $31$
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:  $(1,17,2,16,3,15,4,14,5,13,6,12,7,22,8,21,9,20,10,19,11,18)$, $(1,6,4,7,8)(2,10,9,5,11)(12,21,17,20,15,16,18,22,19,13)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5$:  $C_5$
$8$:  $D_{4}$
$10$:  $D_{5}$, $C_{10}$ x 3
$20$:  $D_{10}$, 20T3
$40$:  20T7, 20T12
$50$:  $D_5\times C_5$
$100$:  20T24
$200$:  20T53

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

44T218, 44T219, 44T220

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

77 x 77 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed