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Properties

Label 30T5025
30T5025 1 3 1->3 25 1->25 2 4 2->4 29 2->29 10 3->10 27 3->27 8 4->8 23 4->23 5 5->2 24 5->24 6 6->1 30 6->30 7 7->5 28 7->28 9 8->9 22 8->22 9->6 26 9->26 10->7 21 10->21 11 11->9 11->21 12 12->5 12->29 13 13->10 13->25 14 14->3 14->30 15 15->4 15->22 16 16->7 16->26 17 17->8 17->24 18 18->2 18->27 19 19->1 19->23 20 20->6 20->28 21->12 21->18 22->17 22->19 23->11 23->13 24->15 25->14 26->20 26->20 27->12 27->16 28->11 28->14 29->15 29->19 30->16 30->18
Degree $30$
Order $2239488000$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $A_6^3.S_4.C_2$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(30, 5025);
 

Group invariants

Abstract group:  $A_6^3.S_4.C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $2239488000=2^{13} \cdot 3^{7} \cdot 5^{3}$
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 $n$:  $30$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $5025$
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:  $(1,25,14,3,27,12,5,24,15,4,23,13,10,21,18,2,29,19)(6,30,16,7,28,11,9,26,20)(8,22,17)$, $(1,3,10,7,5,2,4,8,9,6)(11,21,12,29,15,22,19,23)(13,25)(14,30,18,27,16,26,20,28)(17,24)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$
$48$:  $S_4\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 5: None

Degree 6: None

Degree 10: None

Degree 15: None

Low degree siblings

36T97836

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