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Properties

Label 22T42
22T42 1 8 1->8 2 7 2->7 3 9 3->9 14 3->14 4 10 4->10 13 4->13 5 5->10 5->14 6 6->9 6->13 7->5 8->6 17 9->17 18 10->18 11 11->7 12 12->8 15 13->15 16 14->16 15->12 20 15->20 16->11 19 16->19 17->18 17->19 18->20 19->15 22 19->22 20->16 21 20->21 21->3 21->22 22->4
Degree $22$
Order $1351680$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^{11}.\PSL(2,11)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 42);
 

Group invariants

Abstract group:  $C_2^{11}.\PSL(2,11)$
Copy content magma:IdentifyGroup(G);
 
Order:  $1351680=2^{13} \cdot 3 \cdot 5 \cdot 11$
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 $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $42$
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:  $(1,8)(2,7)(3,14)(4,13)(5,10)(6,9)(15,20,16,19)(17,18)(21,22)$, $(3,9,17,19,22,4,10,18,20,21)(5,14,16,11,7)(6,13,15,12,8)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$660$:  $\PSL(2,11)$
$1320$:  22T13
$675840$:  22T39

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $\PSL(2,11)$

Low degree siblings

22T42, 44T433 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