Properties

Label 35T47
35T47 1 11 1->11 28 1->28 2 12 2->12 27 2->27 3 8 3->8 24 3->24 4 13 4->13 26 4->26 5 14 5->14 25 5->25 6 9 6->9 23 6->23 7 10 7->10 22 7->22 19 8->19 30 8->30 17 9->17 33 9->33 18 10->18 35 10->35 15 11->15 32 11->32 20 12->20 34 12->34 16 13->16 31 13->31 21 14->21 29 14->29 15->12 15->17 16->14 17->10 18->13 18->21 19->9 19->20 20->8 21->11 22->3 22->5 23->4 23->6 24->7 24->7 25->1 25->2 26->1 26->2 27->4 27->6 28->3 28->5 29->27 29->31 30->26 30->34 31->24 31->35 32->28 32->29 33->22 33->30 34->25 34->32 35->23 35->33
Degree $35$
Order $48020$
Cyclic no
Abelian no
Solvable yes
Transitivity $1$
Primitive no
$p$-group no
Group: $C_7^4:F_5$

Related objects

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Show commands: Gap / Magma / Oscar / SageMath

Copy content comment:Define the Galois group
 
Copy content magma:G := TransitiveGroup(35, 47);
 
Copy content sage:G = TransitiveGroup(35, 47)
 
Copy content oscar:G = transitive_group(35, 47)
 
Copy content gap:G := TransitiveGroup(35, 47);
 

Group invariants

Abstract group:  $C_7^4:F_5$
Copy content comment:Abstract group ID
 
Copy content magma:IdentifyGroup(G);
 
Copy content sage:G.id()
 
Copy content oscar:small_group_identification(G)
 
Copy content gap:IdGroup(G);
 
Order:  $48020=2^{2} \cdot 5 \cdot 7^{4}$
Copy content comment:Order
 
Copy content magma:Order(G);
 
Copy content sage:G.order()
 
Copy content oscar:order(G)
 
Copy content gap: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)
 
Copy content gap:IsCyclic(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)
 
Copy content gap:IsAbelian(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)
 
Copy content gap:IsSolvable(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
 
Copy content gap:if IsNilpotentGroup(G) then NilpotencyClassOfGroup(G); fi;
 

Group action invariants

Degree $n$:  $35$
Copy content comment:Degree
 
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Copy content sage:G.degree()
 
Copy content oscar:degree(G)
 
Copy content gap:NrMovedPoints(G);
 
Transitive number $t$:  $47$
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]
 
Copy content gap:TransitiveIdentification(G);
 
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)
 
Copy content gap:ForAll(GeneratorsOfGroup(G), g -> SignPerm(g) = 1);
 
Transitivity:  1
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)
 
Copy content gap:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content comment:Order of the centralizer of G in S_n
 
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Copy content sage:SymmetricGroup(35).centralizer(G).order()
 
Copy content oscar:order(centralizer(symmetric_group(35), G)[1])
 
Copy content gap:Order(Centralizer(SymmetricGroup(35), G));
 
Generators:  $(1,28,3,24,7,22,5,25,2,27,6,23,4,26)(8,19,9,17,10,18,13,16,14,21,11,15,12,20)(29,31,35,33,30,34,32)$, $(1,11,32,28,5,14,29,27,4,13,31,24,7,10,35,23,6,9,33,22,3,8,30,26,2,12,34,25)(15,17)(18,21)(19,20)$
Copy content comment:Generators
 
Copy content magma:Generators(G);
 
Copy content sage:G.gens()
 
Copy content oscar:gens(G)
 
Copy content gap:GeneratorsOfGroup(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$20$:  $F_5$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: $F_5$

Degree 7: None

Low degree siblings

35T46

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)
 
Copy content gap:ConjugacyClasses(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)
 
Copy content gap:CharacterTable(G);
 

Regular extensions

Data not computed