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Properties

Label 24T4587
24T4587 1 3 1->3 11 1->11 2 4 2->4 12 2->12 3->2 9 3->9 4->1 10 4->10 5 6 5->6 14 5->14 13 6->13 7 16 7->16 8 15 8->15 19 9->19 24 9->24 20 10->20 23 10->23 17 11->17 21 11->21 18 12->18 22 12->22 13->18 13->22 14->17 14->21 15->20 15->23 16->19 16->24 17->1 17->13 18->2 18->14 19->4 19->15 20->3 20->16 21->7 22->8 23->5 24->6
Degree $24$
Order $1536$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^6:(C_4\times S_3)$

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Copy content magma:G := TransitiveGroup(24, 4587);
 

Group invariants

Abstract group:  $C_2^6:(C_4\times S_3)$
Copy content magma:IdentifyGroup(G);
 
Order:  $1536=2^{9} \cdot 3$
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 $t$:  $4587$
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:  $(1,11,17)(2,12,18)(3,9,19,4,10,20)(5,14,21,7,16,24,6,13,22,8,15,23)$, $(1,3,2,4)(5,6)(9,24)(10,23)(11,21)(12,22)(13,18,14,17)(15,20,16,19)$
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, $C_2^2$
$6$:  $S_3$
$8$:  $C_4\times C_2$
$12$:  $D_{6}$
$24$:  $S_4$, $S_3 \times C_4$
$48$:  $S_4\times C_2$
$96$:  12T53
$192$:  $V_4^2:(S_3\times C_2)$
$384$:  12T153

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: $S_3$

Degree 4: None

Degree 6: $S_4$

Degree 8: None

Degree 12: 12T110

Low degree siblings

16T1300 x 2, 24T3348 x 2, 24T3353 x 2, 24T4486 x 2, 24T4491 x 2, 24T4584 x 2, 24T4587, 24T4767 x 2, 24T4768 x 2, 32T96743, 32T96757, 32T96808, 32T96822 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{24}$ $1$ $1$ $0$ $()$
2A $2^{8},1^{8}$ $3$ $2$ $8$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)(17,18)(19,20)(21,22)(23,24)$
2B $2^{6},1^{12}$ $4$ $2$ $6$ $( 1, 2)( 3, 4)(13,14)(15,16)(17,18)(19,20)$
2C $2^{12}$ $6$ $2$ $12$ $( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,18)(19,20)(21,22)(23,24)$
2D $2^{8},1^{8}$ $6$ $2$ $8$ $( 9,11)(10,12)(13,15)(14,16)(17,20)(18,19)(21,23)(22,24)$
2E $2^{12}$ $12$ $2$ $12$ $( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,10)(11,12)(13,14)(15,16)(17,22)(18,21)(19,23)(20,24)$
2F $2^{10},1^{4}$ $12$ $2$ $10$ $( 1, 2)( 3, 4)( 9,11)(10,12)(13,16)(14,15)(17,19)(18,20)(21,23)(22,24)$
2G $2^{8},1^{8}$ $12$ $2$ $8$ $( 9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,24)(20,23)$
2H $2^{12}$ $24$ $2$ $12$ $( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,13)(10,14)(11,15)(12,16)(17,23)(18,24)(19,22)(20,21)$
2I $2^{12}$ $24$ $2$ $12$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,21)(10,22)(11,23)(12,24)(13,17)(14,18)(15,20)(16,19)$
2J $2^{10},1^{4}$ $24$ $2$ $10$ $( 5, 6)( 7, 8)( 9,22)(10,21)(11,24)(12,23)(13,17)(14,18)(15,20)(16,19)$
3A $3^{8}$ $128$ $3$ $16$ $( 1,20,14)( 2,19,13)( 3,18,15)( 4,17,16)( 5,24, 9)( 6,23,10)( 7,21,12)( 8,22,11)$
4A1 $4^{3},2^{3},1^{6}$ $16$ $4$ $12$ $( 1, 3, 2, 4)( 7, 8)(11,12)(13,16,14,15)(17,20,18,19)(21,22)$
4A-1 $4^{3},2^{3},1^{6}$ $16$ $4$ $12$ $( 1, 4, 2, 3)( 7, 8)(11,12)(13,15,14,16)(17,19,18,20)(21,22)$
4B $4^{4},1^{8}$ $24$ $4$ $12$ $( 1,23, 2,24)( 3,22, 4,21)( 5,19, 6,20)( 7,17, 8,18)$
4C $4^{4},2^{2},1^{4}$ $24$ $4$ $14$ $( 1, 2)( 3, 4)( 9,13,10,14)(11,15,12,16)(17,22,18,21)(19,23,20,24)$
4D $4^{4},2^{2},1^{4}$ $24$ $4$ $14$ $( 5, 6)( 7, 8)( 9,17,10,18)(11,20,12,19)(13,22,14,21)(15,24,16,23)$
4E $4^{4},2^{4}$ $24$ $4$ $16$ $( 1, 3)( 2, 4)( 5, 8)( 6, 7)( 9,16,10,15)(11,14,12,13)(17,21,18,22)(19,24,20,23)$
4F $4^{4},2^{4}$ $48$ $4$ $16$ $( 1, 4)( 2, 3)( 5, 7)( 6, 8)( 9,21,11,23)(10,22,12,24)(13,18,15,19)(14,17,16,20)$
4G $4^{4},2^{4}$ $48$ $4$ $16$ $( 1, 9, 3,12)( 2,10, 4,11)( 5,14, 7,15)( 6,13, 8,16)(17,20)(18,19)(21,23)(22,24)$
4H1 $4^{5},2,1^{2}$ $48$ $4$ $16$ $( 1, 3, 2, 4)( 5, 6)( 9,19,11,17)(10,20,12,18)(13,22,16,24)(14,21,15,23)$
4H-1 $4^{5},2,1^{2}$ $48$ $4$ $16$ $( 1, 4, 2, 3)( 5, 6)( 9,17,11,19)(10,18,12,20)(13,24,16,22)(14,23,15,21)$
4I1 $4^{3},2^{5},1^{2}$ $48$ $4$ $14$ $( 1,24, 2,23)( 3,22, 4,21)( 5,18)( 6,17)( 7,19)( 8,20)( 9,12,10,11)(15,16)$
4I-1 $4^{3},2^{5},1^{2}$ $48$ $4$ $14$ $( 1,23, 2,24)( 3,21, 4,22)( 5,18)( 6,17)( 7,19)( 8,20)( 9,11,10,12)(15,16)$
4J1 $4^{5},2,1^{2}$ $48$ $4$ $16$ $( 1, 5, 4, 7)( 2, 6, 3, 8)(11,12)(13,15,14,16)(17,21,20,24)(18,22,19,23)$
4J-1 $4^{5},2,1^{2}$ $48$ $4$ $16$ $( 1, 7, 4, 5)( 2, 8, 3, 6)(11,12)(13,16,14,15)(17,24,20,21)(18,23,19,22)$
4K $4^{6}$ $96$ $4$ $18$ $( 1,20, 6,24)( 2,19, 5,23)( 3,18, 8,21)( 4,17, 7,22)( 9,14,10,13)(11,16,12,15)$
4L $4^{4},2^{4}$ $96$ $4$ $16$ $( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,19,13,24)(10,20,14,23)(11,18,15,22)(12,17,16,21)$
6A $6^{2},3^{4}$ $128$ $6$ $18$ $( 1,13,20, 2,14,19)( 3,16,18, 4,15,17)( 5, 9,24)( 6,10,23)( 7,12,21)( 8,11,22)$
8A1 $8^{2},4^{2}$ $96$ $8$ $20$ $( 1, 6, 3, 7)( 2, 5, 4, 8)( 9,21,16,18,10,22,15,17)(11,24,14,20,12,23,13,19)$
8A-1 $8^{2},4^{2}$ $96$ $8$ $20$ $( 1, 7, 3, 6)( 2, 8, 4, 5)( 9,17,15,22,10,18,16,21)(11,19,13,23,12,20,14,24)$
12A1 $12,6,3^{2}$ $128$ $12$ $20$ $( 1,17,13, 3,20,16, 2,18,14, 4,19,15)( 5,24, 9)( 6,23,10)( 7,22,12, 8,21,11)$
12A-1 $12,6,3^{2}$ $128$ $12$ $20$ $( 1,15,19, 4,14,18, 2,16,20, 3,13,17)( 5, 9,24)( 6,10,23)( 7,11,21, 8,12,22)$

Malle's constant $a(G)$:     $1/6$

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Character table

33 x 33 character table

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Regular extensions

Data not computed