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Properties

Label 26T23
26T23 1 11 1->11 20 1->20 2 22 2->22 3 6 3->6 24 3->24 4 10 4->10 26 4->26 5 5->1 15 5->15 6->5 17 6->17 7 9 7->9 19 7->19 8 13 8->13 21 8->21 9->4 23 9->23 10->8 25 10->25 12 11->12 14 11->14 12->3 16 12->16 13->7 18 13->18 14->9 14->15 15->3 15->25 16->10 16->22 17->4 17->19 18->11 18->16 19->5 19->26 20->12 20->23 21->6 21->20 22->13 22->17 23->7 23->14 24->1 25->8 25->21 26->2 26->18
Degree $26$
Order $2028$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{13}^2:D_6$

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Copy content magma:G := TransitiveGroup(26, 23);
 

Group invariants

Abstract group:  $C_{13}^2:D_6$
Copy content magma:IdentifyGroup(G);
 
Order:  $2028=2^{2} \cdot 3 \cdot 13^{2}$
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 $t$:  $23$
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:  $(1,11,12,3,6,5)(4,10,8,13,7,9)(14,15,25,21,20,23)(16,22,17,19,26,18)$, $(1,20,12,16,10,25,8,21,6,17,4,26,2,22,13,18,11,14,9,23,7,19,5,15,3,24)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

39T34 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 $1^{26}$ $1$ $1$ $0$ $()$
2A $2^{13}$ $39$ $2$ $13$ $( 1,25)( 2,20)( 3,15)( 4,23)( 5,18)( 6,26)( 7,21)( 8,16)( 9,24)(10,19)(11,14)(12,22)(13,17)$
2B $2^{13}$ $39$ $2$ $13$ $( 1,20)( 2,25)( 3,17)( 4,22)( 5,14)( 6,19)( 7,24)( 8,16)( 9,21)(10,26)(11,18)(12,23)(13,15)$
2C $2^{12},1^{2}$ $169$ $2$ $12$ $( 1,11)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,13)(14,20)(15,19)(16,18)(21,26)(22,25)(23,24)$
3A $3^{8},1^{2}$ $338$ $3$ $16$ $( 1,13, 4)( 2, 9, 7)( 3, 5,10)( 8,11,12)(14,21,16)(15,24,25)(18,20,26)(19,23,22)$
6A $6^{4},1^{2}$ $338$ $6$ $20$ $( 1, 8,13,11, 4,12)( 2, 5, 9,10, 7, 3)(14,18,21,20,16,26)(15,22,24,19,25,23)$
13A1 $13^{2}$ $6$ $13$ $24$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,25,23,21,19,17,15,26,24,22,20,18,16)$
13A2 $13^{2}$ $6$ $13$ $24$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,23,19,15,24,20,16,25,21,17,26,22,18)$
13A3 $13^{2}$ $6$ $13$ $24$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,21,15,22,16,23,17,24,18,25,19,26,20)$
13A4 $13^{2}$ $6$ $13$ $24$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,19,24,16,21,26,18,23,15,20,25,17,22)$
13A5 $13^{2}$ $6$ $13$ $24$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,17,20,23,26,16,19,22,25,15,18,21,24)$
13A6 $13^{2}$ $6$ $13$ $24$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,15,16,17,18,19,20,21,22,23,24,25,26)$
13B1 $13^{2}$ $6$ $13$ $24$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,20,26,19,25,18,24,17,23,16,22,15,21)$
13B2 $13^{2}$ $6$ $13$ $24$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,26,25,24,23,22,21,20,19,18,17,16,15)$
13B3 $13^{2}$ $6$ $13$ $24$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,19,24,16,21,26,18,23,15,20,25,17,22)$
13B4 $13^{2}$ $6$ $13$ $24$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,25,23,21,19,17,15,26,24,22,20,18,16)$
13B5 $13^{2}$ $6$ $13$ $24$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,18,22,26,17,21,25,16,20,24,15,19,23)$
13B6 $13^{2}$ $6$ $13$ $24$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,24,21,18,15,25,22,19,16,26,23,20,17)$
13C1 $13,1^{13}$ $12$ $13$ $12$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)$
13C2 $13,1^{13}$ $12$ $13$ $12$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)$
13D1 $13^{2}$ $12$ $13$ $24$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,20,26,19,25,18,24,17,23,16,22,15,21)$
13D2 $13^{2}$ $12$ $13$ $24$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,20,26,19,25,18,24,17,23,16,22,15,21)$
13D3 $13^{2}$ $12$ $13$ $24$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,17,20,23,26,16,19,22,25,15,18,21,24)$
13D4 $13^{2}$ $12$ $13$ $24$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,24,21,18,15,25,22,19,16,26,23,20,17)$
13D5 $13^{2}$ $12$ $13$ $24$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,26,25,24,23,22,21,20,19,18,17,16,15)$
13D6 $13^{2}$ $12$ $13$ $24$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,18,22,26,17,21,25,16,20,24,15,19,23)$
26A1 $26$ $78$ $26$ $25$ $( 1,24, 4,22, 7,20,10,18,13,16, 3,14, 6,25, 9,23,12,21, 2,19, 5,17, 8,15,11,26)$
26A3 $26$ $78$ $26$ $25$ $( 1,22,10,16, 6,23, 2,17,11,24, 7,18, 3,25,12,19, 8,26, 4,20,13,14, 9,21, 5,15)$
26A5 $26$ $78$ $26$ $25$ $( 1,20, 3,23, 5,26, 7,16, 9,19,11,22,13,25, 2,15, 4,18, 6,21, 8,24,10,14,12,17)$
26A7 $26$ $78$ $26$ $25$ $( 1,18, 9,17, 4,16,12,15, 7,14, 2,26,10,25, 5,24,13,23, 8,22, 3,21,11,20, 6,19)$
26A9 $26$ $78$ $26$ $25$ $( 1,16, 2,24, 3,19, 4,14, 5,22, 6,17, 7,25, 8,20, 9,15,10,23,11,18,12,26,13,21)$
26A11 $26$ $78$ $26$ $25$ $( 1,14, 8,18, 2,22, 9,26, 3,17,10,21, 4,25,11,16, 5,20,12,24, 6,15,13,19, 7,23)$
26B1 $26$ $78$ $26$ $25$ $( 1,23,10,16, 6,22, 2,15,11,21, 7,14, 3,20,12,26, 8,19, 4,25,13,18, 9,24, 5,17)$
26B3 $26$ $78$ $26$ $25$ $( 1,16, 2,21, 3,26, 4,18, 5,23, 6,15, 7,20, 8,25, 9,17,10,22,11,14,12,19,13,24)$
26B5 $26$ $78$ $26$ $25$ $( 1,22, 7,26,13,17, 6,21,12,25, 5,16,11,20, 4,24,10,15, 3,19, 9,23, 2,14, 8,18)$
26B7 $26$ $78$ $26$ $25$ $( 1,15,12,18,10,21, 8,24, 6,14, 4,17, 2,20,13,23,11,26, 9,16, 7,19, 5,22, 3,25)$
26B9 $26$ $78$ $26$ $25$ $( 1,21, 4,23, 7,25,10,14,13,16, 3,18, 6,20, 9,22,12,24, 2,26, 5,15, 8,17,11,19)$
26B11 $26$ $78$ $26$ $25$ $( 1,14, 9,15, 4,16,12,17, 7,18, 2,19,10,20, 5,21,13,22, 8,23, 3,24,11,25, 6,26)$

Malle's constant $a(G)$:     $1/12$

Copy content magma:ConjugacyClasses(G);
 

Character table

38 x 38 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed