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Properties

Label 26T29
26T29 1 2 1->2 26 1->26 19 2->19 3 13 3->13 25 3->25 4 12 4->12 18 4->18 5 11 5->11 24 5->24 6 10 6->10 17 6->17 7 9 7->9 23 7->23 8 16 8->16 22 9->22 15 10->15 21 11->21 14 12->14 20 13->20 14->10 14->26 15->9 15->25 16->24 17->7 17->23 18->6 18->22 19->5 19->21 20->4 21->3 22->2 23->1 24->13 25->12 26->11
Degree $26$
Order $4056$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{13}^2:C_{24}$

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Copy content magma:G := TransitiveGroup(26, 29);
 

Group invariants

Abstract group:  $C_{13}^2:C_{24}$
Copy content magma:IdentifyGroup(G);
 
Order:  $4056=2^{3} \cdot 3 \cdot 13^{2}$
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 $n$:  $26$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $29$
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:  $(1,2)(3,13)(4,12)(5,11)(6,10)(7,9)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)$, $(1,26,11,21,3,25,12,14,10,15,9,22,2,19,5,24,13,20,4,18,6,17,7,23)(8,16)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$4$:  $C_4$
$6$:  $C_6$
$8$:  $C_8$
$12$:  $C_{12}$
$24$:  $C_{24}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

26T29 x 6

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{26}$ $1$ $1$ $0$ $()$
2A $2^{12},1^{2}$ $169$ $2$ $12$ $( 1, 6)( 2, 5)( 3, 4)( 7,13)( 8,12)( 9,11)(14,19)(15,18)(16,17)(20,26)(21,25)(22,24)$
3A1 $3^{8},1^{2}$ $169$ $3$ $16$ $( 1, 7, 9)( 2, 3,12)( 4, 8, 5)( 6,13,11)(14,20,22)(15,16,25)(17,21,18)(19,26,24)$
3A-1 $3^{8},1^{2}$ $169$ $3$ $16$ $( 1, 9, 7)( 2,12, 3)( 4, 5, 8)( 6,11,13)(14,22,20)(15,25,16)(17,18,21)(19,24,26)$
4A1 $4^{6},1^{2}$ $169$ $4$ $18$ $( 1, 3, 6, 4)( 2,11, 5, 9)( 7,12,13, 8)(14,16,19,17)(15,24,18,22)(20,25,26,21)$
4A-1 $4^{6},1^{2}$ $169$ $4$ $18$ $( 1, 4, 6, 3)( 2, 9, 5,11)( 7, 8,13,12)(14,17,19,16)(15,22,18,24)(20,21,26,25)$
6A1 $6^{4},1^{2}$ $169$ $6$ $20$ $( 1,11, 7, 6, 9,13)( 2, 8, 3, 5,12, 4)(14,24,20,19,22,26)(15,21,16,18,25,17)$
6A-1 $6^{4},1^{2}$ $169$ $6$ $20$ $( 1,13, 9, 6, 7,11)( 2, 4,12, 5, 3, 8)(14,26,22,19,20,24)(15,17,25,18,16,21)$
8A1 $8^{3},2$ $169$ $8$ $22$ $( 1,18, 3,22, 6,15, 4,24)( 2,20,11,25, 5,26, 9,21)( 7,17,12,14,13,16, 8,19)(10,23)$
8A-1 $8^{3},2$ $169$ $8$ $22$ $( 1,24, 4,15, 6,22, 3,18)( 2,21, 9,26, 5,25,11,20)( 7,19, 8,16,13,14,12,17)(10,23)$
8A3 $8^{3},2$ $169$ $8$ $22$ $( 1,22, 4,18, 6,24, 3,15)( 2,25, 9,20, 5,21,11,26)( 7,14, 8,17,13,19,12,16)(10,23)$
8A-3 $8^{3},2$ $169$ $8$ $22$ $( 1,15, 3,24, 6,18, 4,22)( 2,26,11,21, 5,20, 9,25)( 7,16,12,19,13,17, 8,14)(10,23)$
12A1 $12^{2},1^{2}$ $169$ $12$ $22$ $( 1, 8,11, 3, 7, 5, 6,12, 9, 4,13, 2)(14,21,24,16,20,18,19,25,22,17,26,15)$
12A-1 $12^{2},1^{2}$ $169$ $12$ $22$ $( 1, 2,13, 4, 9,12, 6, 5, 7, 3,11, 8)(14,15,26,17,22,25,19,18,20,16,24,21)$
12A5 $12^{2},1^{2}$ $169$ $12$ $22$ $( 1, 5,13, 3, 9, 8, 6, 2, 7, 4,11,12)(14,18,26,16,22,21,19,15,20,17,24,25)$
12A-5 $12^{2},1^{2}$ $169$ $12$ $22$ $( 1,12,11, 4, 7, 2, 6, 8, 9, 3,13, 5)(14,25,24,17,20,15,19,21,22,16,26,18)$
13A $13^{2}$ $24$ $13$ $24$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,21,15,22,16,23,17,24,18,25,19,26,20)$
13B $13^{2}$ $24$ $13$ $24$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,23,19,15,24,20,16,25,21,17,26,22,18)$
13C $13^{2}$ $24$ $13$ $24$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,17,20,23,26,16,19,22,25,15,18,21,24)$
13D $13^{2}$ $24$ $13$ $24$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,24,21,18,15,25,22,19,16,26,23,20,17)$
13E $13^{2}$ $24$ $13$ $24$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,26,25,24,23,22,21,20,19,18,17,16,15)$
13F $13,1^{13}$ $24$ $13$ $12$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)$
13G $13^{2}$ $24$ $13$ $24$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,16,18,20,22,24,26,15,17,19,21,23,25)$
24A1 $24,2$ $169$ $24$ $24$ $( 1,20, 8,18,11,19, 3,25, 7,22, 5,17, 6,26,12,15, 9,14, 4,21,13,24, 2,16)(10,23)$
24A-1 $24,2$ $169$ $24$ $24$ $( 1,16, 2,24,13,21, 4,14, 9,15,12,26, 6,17, 5,22, 7,25, 3,19,11,18, 8,20)(10,23)$
24A5 $24,2$ $169$ $24$ $24$ $( 1,19, 5,15,13,20, 3,17, 9,24, 8,25, 6,14, 2,18, 7,26, 4,16,11,22,12,21)(10,23)$
24A-5 $24,2$ $169$ $24$ $24$ $( 1,21,12,22,11,16, 4,26, 7,18, 2,14, 6,25, 8,24, 9,17, 3,20,13,15, 5,19)(10,23)$
24A7 $24,2$ $169$ $24$ $24$ $( 1,25,12,24,11,17, 4,20, 7,15, 2,19, 6,21, 8,22, 9,16, 3,26,13,18, 5,14)(10,23)$
24A-7 $24,2$ $169$ $24$ $24$ $( 1,14, 5,18,13,26, 3,16, 9,22, 8,21, 6,19, 2,15, 7,20, 4,17,11,24,12,25)(10,23)$
24A11 $24,2$ $169$ $24$ $24$ $( 1,17, 2,22,13,25, 4,19, 9,18,12,20, 6,16, 5,24, 7,21, 3,14,11,15, 8,26)(10,23)$
24A-11 $24,2$ $169$ $24$ $24$ $( 1,26, 8,15,11,14, 3,21, 7,24, 5,16, 6,20,12,18, 9,19, 4,25,13,22, 2,17)(10,23)$

Malle's constant $a(G)$:     $1/12$

Copy content magma:ConjugacyClasses(G);
 

Character table

31 x 31 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed