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Properties

Label 35T260
35T260 1 10 1->10 23 1->23 2 6 2->6 22 2->22 3 7 3->7 21 3->21 4 8 4->8 25 4->25 5 9 5->9 24 5->24 17 6->17 6->22 16 7->16 7->23 20 8->20 8->24 19 9->19 9->25 18 10->18 10->21 11 11->4 12 11->12 12->3 13 12->13 13->2 14 13->14 14->1 15 14->15 15->5 15->11 16->17 28 16->28 17->18 27 17->27 18->19 26 18->26 19->20 30 19->30 20->16 29 20->29 21->2 21->11 22->3 22->15 23->4 23->14 24->5 24->13 25->1 25->12 31 26->31 34 26->34 35 27->35 27->35 28->31 28->34 32 29->32 33 29->33 30->32 30->33 31->6 32->10 33->9 34->8 35->7
Degree $35$
Order $787500000$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_5^6.(D_5\times S_7)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(35, 260);
 

Group invariants

Abstract group:  $C_5^6.(D_5\times S_7)$
Copy content magma:IdentifyGroup(G);
 
Order:  $787500000=2^{5} \cdot 3^{2} \cdot 5^{8} \cdot 7$
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 $n$:  $35$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $260$
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:  $(1,23,14)(2,22,15,5,24,13)(3,21,11,4,25,12)(6,17,27,35,7,16,28,34,8,20,29,33,9,19,30,32,10,18,26,31)$, $(1,10,21,2,6,22,3,7,23,4,8,24,5,9,25)(11,12,13,14,15)(16,17,18,19,20)(26,34)(27,35)(28,31)(29,32)(30,33)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$10$:  $D_{5}$
$20$:  $D_{10}$
$5040$:  $S_7$
$10080$:  $S_7\times C_2$
$50400$:  35T49
$157500000$:  35T217

Resolvents shown for degrees $\leq 47$

Subfields

Degree 5: None

Degree 7: $S_7$

Low degree siblings

35T260 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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed