↑

Properties

Label 22T36
22T36 1 6 1->6 15 1->15 2 5 2->5 16 2->16 3 3->1 3->2 4 4->1 4->2 10 5->10 20 5->20 9 6->9 19 6->19 7 7->15 17 7->17 8 8->16 18 8->18 9->3 11 9->11 10->4 12 10->12 11->7 11->12 12->8 13 13->3 13->20 14 14->4 14->19 15->5 21 15->21 16->6 22 16->22 17->14 18->13 19->14 19->22 20->13 20->21 21->7 21->10 22->8 22->9
Degree $22$
Order $112640$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{10}.C_{11}:C_{10}$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(22, 36);
 

Group invariants

Abstract group:  $C_2^{10}.C_{11}:C_{10}$
Copy content magma:IdentifyGroup(G);
 
Order:  $112640=2^{11} \cdot 5 \cdot 11$
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 $t$:  $36$
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:  $(1,15,5,10,4,2,16,6,9,3)(7,17,14,19,22,8,18,13,20,21)(11,12)$, $(1,6,19,14,4)(2,5,20,13,3)(7,15,21,10,12,8,16,22,9,11)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$10$:  $C_{10}$
$55$:  $C_{11}:C_5$
$110$:  22T5
$56320$:  22T33

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $C_{11}:C_5$

Low degree siblings

22T36 x 2, 44T314 x 3, 44T315 x 3

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

80 x 80 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed