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Properties

Label 24T5384
24T5384 1 9 1->9 13 1->13 24 1->24 2 10 2->10 14 2->14 23 2->23 3 11 3->11 15 3->15 22 3->22 4 12 4->12 16 4->16 21 4->21 5 5->11 5->16 19 5->19 6 6->12 6->15 20 6->20 7 7->10 7->13 17 7->17 8 8->9 8->14 18 8->18 9->2 9->7 9->11 10->1 10->8 10->12 11->4 11->6 12->3 12->5 13->2 13->16 14->1 14->15 15->4 16->3 17->8 17->20 17->20 18->7 18->19 18->19 19->6 19->17 20->5 20->18 21->3 21->23 21->23 22->4 22->24 22->24 23->1 23->22 24->2 24->21
Degree $24$
Order $3072$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^7:S_4$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(24, 5384);
 

Group invariants

Abstract group:  $C_2^7:S_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $3072=2^{10} \cdot 3$
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 $t$:  $5384$
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:  $(1,9,2,10)(3,11,4,12)(5,16)(6,15)(7,13)(8,14)(17,20,18,19)(21,23,22,24)$, $(1,13,2,14)(3,15,4,16)(5,11,6,12)(7,10,8,9)(17,20)(18,19)(21,23)(22,24)$, $(1,24,2,23)(3,22,4,21)(5,19,6,20)(7,17,8,18)(9,11)(10,12)(13,16)(14,15)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$6$:  $S_3$
$8$:  $C_2^3$
$12$:  $D_{6}$ x 3
$24$:  $S_4$ x 3, $S_3 \times C_2^2$
$48$:  $S_4\times C_2$ x 9
$96$:  $V_4^2:S_3$, 12T48 x 3
$192$:  12T100 x 3
$384$:  12T139, 16T751 x 2
$768$:  16T1063, 32T34928
$1536$:  24T3330

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_3$, $S_4$, $S_4$

Degree 8: None

Degree 12: $S_4$

Low degree siblings

24T5377 x 4, 24T5384 x 3, 24T5435 x 4, 24T5444 x 4, 24T5591 x 4, 24T5593 x 4, 24T5731 x 4, 24T5744 x 4, 24T6285 x 4, 24T6428 x 4, 24T6790 x 4, 24T6812 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

62 x 62 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed