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Properties

Label 33T116
33T116 1 18 1->18 25 1->25 2 16 2->16 27 2->27 3 17 3->17 26 3->26 4 7 4->7 8 4->8 5 5->8 9 5->9 6 6->7 6->9 24 7->24 29 7->29 22 8->22 28 8->28 23 9->23 30 9->30 10 10->3 20 10->20 11 11->2 19 11->19 12 12->1 21 12->21 13 31 13->31 32 13->32 14 14->32 33 14->33 15 15->31 15->33 16->2 16->20 17->1 17->19 18->3 18->21 19->13 19->15 20->14 20->15 21->13 21->14 22->4 22->11 23->5 23->10 24->6 24->12 25->22 25->29 26->24 26->30 27->23 27->28 28->18 29->17 30->16 31->4 31->10 32->5 32->12 33->6 33->11
Degree $33$
Order $1403004240$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_3^{11}.M_{11}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(33, 116);
 

Group invariants

Abstract group:  $C_3^{11}.M_{11}$
Copy content magma:IdentifyGroup(G);
 
Order:  $1403004240=2^{4} \cdot 3^{13} \cdot 5 \cdot 11$
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 $n$:  $33$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $116$
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:  $(1,18,21,14,32,12)(2,16,20,15,33,11)(3,17,19,13,31,10)(4,7,24,6,9,23,5,8,22)(25,29)(26,30)(27,28)$, $(1,25,22,11,19,15,31,4,8,28,18,3,26,24,12,21,13,32,5,9,30,16,2,27,23,10,20,14,33,6,7,29,17)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$7920$:  $M_{11}$
$5773680$:  36T55017

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 11: $M_{11}$

Low degree siblings

There are no siblings 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