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Properties

Label 24T9971
24T9971 1 11 1->11 24 1->24 2 12 2->12 23 2->23 3 8 3->8 21 3->21 4 7 4->7 22 4->22 5 10 5->10 20 5->20 6 9 6->9 19 6->19 16 7->16 7->22 15 8->15 8->21 14 9->14 9->24 13 10->13 10->23 17 11->17 11->19 18 12->18 12->20 13->1 13->14 14->2 15->5 15->16 16->6 17->4 17->18 18->3 19->3 19->12 20->4 20->11 21->6 21->10 22->5 22->9 23->2 23->8 24->1 24->7
Degree $24$
Order $10368$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $(C_2\times C_6^3):S_4$

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Copy content magma:G := TransitiveGroup(24, 9971);
 

Group invariants

Abstract group:  $(C_2\times C_6^3):S_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $10368=2^{7} \cdot 3^{4}$
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 $n$:  $24$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9971$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,24,7,16,6,19,12,18,3,21,10,13)(2,23,8,15,5,20,11,17,4,22,9,14)$, $(1,11,19,3,8,21,6,9,24)(2,12,20,4,7,22,5,10,23)(13,14)(15,16)(17,18)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$
$24$:  $S_4$
$48$:  $S_4\times C_2$
$192$:  $V_4^2:(S_3\times C_2)$
$384$:  $C_2 \wr S_4$
$648$:  $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$
$1296$:  18T301
$5184$:  36T5805

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 4: $S_4$

Degree 6: None

Degree 8: $C_2 \wr S_4$

Degree 12: 12T177

Low degree siblings

24T9971 x 7, 24T9972 x 4

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

69 x 69 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed