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Properties

Label 24T19561
24T19561 1 13 1->13 21 1->21 2 14 2->14 22 2->22 3 18 3->18 19 3->19 4 17 4->17 20 4->20 5 15 5->15 24 5->24 6 16 6->16 23 6->23 7 7->15 7->19 8 8->16 8->20 9 9->13 9->21 10 10->14 10->22 11 11->18 11->23 12 12->17 12->24 15->3 15->12 16->4 16->11 17->6 17->8 18->5 18->7 19->5 19->9 20->6 20->10 21->2 21->8 22->1 22->7 23->4 23->12 24->3 24->11
Degree $24$
Order $331776$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9.C_3^4:Q_8$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(24, 19561);
 

Group invariants

Abstract group:  $C_2^9.C_3^4:Q_8$
Copy content magma:IdentifyGroup(G);
 
Order:  $331776=2^{12} \cdot 3^{4}$
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 $t$:  $19561$
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:  $(1,21,2,22)(3,19,5,24)(4,20,6,23)(7,15,12,17,8,16,11,18)(9,13)(10,14)$, $(1,13)(2,14)(3,18,5,15)(4,17,6,16)(7,19,9,21,8,20,10,22)(11,23,12,24)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $D_{4}$, $C_4\times C_2$, $Q_8$
$16$:  $C_4:C_4$
$72$:  $C_3^2:Q_8$ x 4
$144$:  24T258 x 4
$648$:  12T174
$1296$:  24T2869
$165888$:  16T1898

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 3: None

Degree 4: $C_2^2$

Degree 6: None

Degree 8: None

Degree 12: 12T174

Low degree siblings

24T19560, 32T2267402, 32T2267403, 36T28082 x 2, 36T28084 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

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed