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Properties

Label 35T91
35T91 1 13 1->13 29 1->29 2 12 2->12 28 2->28 3 11 3->11 27 3->27 4 15 4->15 26 4->26 5 14 5->14 30 5->30 6 31 6->31 33 6->33 7 32 7->32 35 7->35 8 8->31 34 8->34 9 9->33 9->35 10 10->32 10->34 11->2 20 11->20 12->1 19 12->19 13->5 18 13->18 14->4 17 14->17 15->3 16 15->16 16->4 16->9 17->3 17->8 18->2 18->7 19->1 19->6 20->5 20->10 21 21->11 23 21->23 22 22->15 23->14 24 24->13 25 24->25 25->12 26->10 26->17 27->9 27->16 28->8 28->20 29->7 29->19 30->6 30->18 31->23 31->29 32->22 32->28 33->21 33->27 34->25 34->26 35->24 35->30
Degree $35$
Order $656250$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5^6:C_7:C_6$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(35, 91);
 

Group invariants

Abstract group:  $C_5^6:C_7:C_6$
Copy content magma:IdentifyGroup(G);
 
Order:  $656250=2 \cdot 3 \cdot 5^{6} \cdot 7$
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 $n$:  $35$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $91$
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:  $(1,13,18,2,12,19)(3,11,20,5,14,17)(4,15,16)(6,33,27,9,35,30)(7,32,28,8,31,29)(10,34,26)(21,23)(24,25)$, $(1,29,19,6,31,23,14,4,26,17,8,34,25,12)(2,28,20,10,32,22,15,3,27,16,9,33,21,11)(5,30,18,7,35,24,13)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$21$:  $C_7:C_3$
$42$:  $(C_7:C_3) \times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: None

Degree 7: $C_7:C_3$

Low degree siblings

35T91 x 5

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