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Properties

Label 22T7
22T7 1 14 1->14 1->14 2 21 2->21 2->21 3 17 3->17 3->17 4 13 4->13 4->13 5 20 5->20 5->20 6 16 6->16 6->16 7 12 7->12 7->12 8 19 8->19 8->19 9 15 9->15 9->15 10 22 10->22 10->22 11 18 11->18 11->18 12->1 13->9 14->6 15->3 16->11 17->8 18->5 19->2 20->10 21->7 22->4
Degree $22$
Order $242$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}\times D_{11}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 7);
 

Group invariants

Abstract group:  $C_{11}\times D_{11}$
Copy content magma:IdentifyGroup(G);
 
Order:  $242=2 \cdot 11^{2}$
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 $t$:  $7$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $11$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,14,6,16,11,18,5,20,10,22,4,13,9,15,3,17,8,19,2,21,7,12)$, $(1,14)(2,21)(3,17)(4,13)(5,20)(6,16)(7,12)(8,19)(9,15)(10,22)(11,18)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T7 x 4

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