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Properties

Label 46T35
46T35 1 18 1->18 26 1->26 2 17 2->17 25 2->25 3 11 3->11 34 3->34 4 12 4->12 33 4->33 5 41 5->41 6 42 6->42 7 7->3 45 7->45 8 8->4 46 8->46 9 9->12 40 9->40 10 10->11 39 10->39 19 11->19 11->34 20 12->20 12->33 13 27 13->27 28 13->28 14 14->27 14->28 15 22 15->22 36 15->36 16 21 16->21 35 16->35 17->16 44 17->44 18->15 43 18->43 19->6 19->10 20->5 20->9 21->4 21->14 22->3 22->13 23 23->22 23->44 24 24->21 24->43 29 25->29 38 25->38 30 26->30 37 26->37 32 27->32 27->38 31 28->31 28->37 29->26 29->46 30->25 30->45 31->7 31->20 32->8 32->19 33->13 33->16 34->14 34->15 35->7 35->23 36->8 36->24 37->1 37->32 38->2 38->31 39->42 40->41 41->1 41->35 42->2 42->36 43->10 43->29 44->9 44->30 45->18 45->23 46->17 46->24
Degree $46$
Order $2122317824$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{22}.F_{23}$

Related objects

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Show commands: Magma / Oscar / SageMath

Copy content comment:Define the Galois group
 
Copy content magma:G := TransitiveGroup(46, 35);
 
Copy content sage:G = TransitiveGroup(46, 35)
 
Copy content oscar:G = transitive_group(46, 35)
 

Group invariants

Abstract group:  $C_2^{22}.F_{23}$
Copy content comment:Abstract group ID
 
Copy content magma:IdentifyGroup(G);
 
Copy content sage:G.id()
 
Order:  $2122317824=2^{23} \cdot 11 \cdot 23$
Copy content comment:Order
 
Copy content magma:Order(G);
 
Copy content sage:G.order()
 
Copy content oscar:order(G)
 
Cyclic:  no
Copy content comment:Determine if group is cyclic
 
Copy content magma:IsCyclic(G);
 
Copy content sage:G.is_cyclic()
 
Copy content oscar:is_cyclic(G)
 
Abelian:  no
Copy content comment:Determine if group is abelian
 
Copy content magma:IsAbelian(G);
 
Copy content sage:G.is_abelian()
 
Copy content oscar:is_abelian(G)
 
Solvable:  yes
Copy content comment:Determine if group is solvable
 
Copy content magma:IsSolvable(G);
 
Copy content sage:G.is_solvable()
 
Copy content oscar:is_solvable(G)
 
Nilpotency class:   not nilpotent
Copy content comment:Nilpotency class
 
Copy content magma:NilpotencyClass(G);
 
Copy content sage:libgap(G).NilpotencyClassOfGroup() if G.is_nilpotent() else -1
 
Copy content oscar:if is_nilpotent(G) nilpotency_class(G) end
 

Group action invariants

Degree $n$:  $46$
Copy content comment:Degree
 
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Copy content sage:G.degree()
 
Copy content oscar:degree(G)
 
Transitive number $t$:  $35$
Copy content comment:Transitive number
 
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Copy content sage:G.transitive_number()
 
Copy content oscar:transitive_group_identification(G)[2]
 
Parity:  $1$
Copy content comment:Parity
 
Copy content magma:IsEven(G);
 
Copy content sage:all(g.SignPerm() == 1 for g in libgap(G).GeneratorsOfGroup())
 
Copy content oscar:is_even(G)
 
Primitive:  no
Copy content comment:Determine if group is primitive
 
Copy content magma:IsPrimitive(G);
 
Copy content sage:G.is_primitive()
 
Copy content oscar:is_primitive(G)
 
$\card{\Aut(F/K)}$:  $2$
Copy content comment:Order of the centralizer of G in S_n
 
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Copy content sage:SymmetricGroup(46).centralizer(G).order()
 
Copy content oscar:order(centralizer(symmetric_group(46), G)[1])
 
Generators:  $(1,18,15,22,3,11,34,14,27,32,19,10,39,42,36,8,46,24,43,29,26,37)(2,17,16,21,4,12,33,13,28,31,20,9,40,41,35,7,45,23,44,30,25,38)$, $(1,26,30,45,18,43,10,11,19,6,42,2,25,29,46,17,44,9,12,20,5,41)(3,34,15,36,24,21,14,28,37,32,8,4,33,16,35,23,22,13,27,38,31,7)$
Copy content comment:Generators
 
Copy content magma:Generators(G);
 
Copy content sage:G.gens()
 
Copy content oscar:gens(G)
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  22T1
$506$:  $F_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $F_{23}$

Low degree siblings

46T36

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 comment:Conjugacy classes
 
Copy content magma:ConjugacyClasses(G);
 
Copy content sage:G.conjugacy_classes()
 
Copy content oscar:conjugacy_classes(G)
 

Character table

Character table not computed

Copy content comment:Character table
 
Copy content magma:CharacterTable(G);
 
Copy content sage:G.character_table()
 
Copy content oscar:character_table(G)
 

Regular extensions

Data not computed