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Properties

Label 26T47
Degree $26$
Order $11232$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $\GL(3,3)$

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Show commands: Magma

magma: G := TransitiveGroup(26, 47);
 

Group action invariants

Degree $n$:  $26$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $47$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $\GL(3,3)$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,14,6,17,12,7,22,20)(2,13,5,18,11,8,21,19)(3,24,16,25,4,23,15,26)(9,10), (1,3,26,7,16,13,22,5)(2,4,25,8,15,14,21,6)(9,17,20,24,10,18,19,23)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$5616$:  $\PSL(3,3)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 13: $\PSL(3,3)$

Low degree siblings

26T47, 26T48 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
$1^{26}$ $1$ $1$ $()$
$2^{13}$ $1$ $2$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22) (23,24)(25,26)$
$6^{4},2$ $624$ $6$ $( 1,14, 9, 2,13,10)( 3, 4)( 5,19,17, 6,20,18)( 7,12,21, 8,11,22) (15,23,26,16,24,25)$
$3^{8},1^{2}$ $624$ $3$ $( 1,13, 9)( 2,14,10)( 5,20,17)( 6,19,18)( 7,11,21)( 8,12,22)(15,24,26) (16,23,25)$
$6^{3},2^{4}$ $104$ $6$ $( 1,20, 8, 2,19, 7)( 3, 4)( 5,22,10, 6,21, 9)(11,13,17,12,14,18)(15,16)(23,24) (25,26)$
$3^{6},1^{8}$ $104$ $3$ $( 1,19, 8)( 2,20, 7)( 5,21,10)( 6,22, 9)(11,14,17)(12,13,18)$
$2^{9},1^{8}$ $117$ $2$ $( 5,11)( 6,12)( 9,18)(10,17)(13,22)(14,21)(15,25)(16,26)(23,24)$
$2^{12},1^{2}$ $117$ $2$ $( 1, 2)( 3, 4)( 5,12)( 6,11)( 7, 8)( 9,17)(10,18)(13,21)(14,22)(15,26)(16,25) (19,20)$
$6^{2},3^{2},2^{3},1^{2}$ $936$ $6$ $( 1,19, 8)( 2,20, 7)( 5,14,10,11,21,17)( 6,13, 9,12,22,18)(15,25)(16,26) (23,24)$
$6^{3},2^{3},1^{2}$ $936$ $6$ $( 1,20, 8, 2,19, 7)( 3, 4)( 5,13,10,12,21,18)( 6,14, 9,11,22,17)(15,26)(16,25)$
$4^{6},2$ $702$ $4$ $( 1, 8, 2, 7)( 3,19, 4,20)( 5,22,12,14)( 6,21,11,13)( 9,25,17,16)(10,26,18,15) (23,24)$
$4^{6},1^{2}$ $702$ $4$ $( 1, 7, 2, 8)( 3,20, 4,19)( 5,21,12,13)( 6,22,11,14)( 9,26,17,15)(10,25,18,16)$
$8^{3},1^{2}$ $702$ $8$ $( 1,20, 7, 4, 2,19, 8, 3)( 5,25,21,18,12,16,13,10)( 6,26,22,17,11,15,14, 9)$
$8^{3},2$ $702$ $8$ $( 1,19, 7, 3, 2,20, 8, 4)( 5,26,21,17,12,15,13, 9)( 6,25,22,18,11,16,14,10) (23,24)$
$8^{3},1^{2}$ $702$ $8$ $( 1, 3, 8,19, 2, 4, 7,20)( 5,10,13,16,12,18,21,25)( 6, 9,14,15,11,17,22,26)$
$8^{3},2$ $702$ $8$ $( 1, 4, 8,20, 2, 3, 7,19)( 5, 9,13,15,12,17,21,26)( 6,10,14,16,11,18,22,25) (23,24)$
$26$ $432$ $26$ $( 1, 5, 7,19,14,26,11, 4,16, 9,22,18,24, 2, 6, 8,20,13,25,12, 3,15,10,21,17,23 )$
$13^{2}$ $432$ $13$ $( 1, 6, 7,20,14,25,11, 3,16,10,22,17,24)( 2, 5, 8,19,13,26,12, 4,15, 9,21,18, 23)$
$26$ $432$ $26$ $( 1,15,20,18,11, 5,10,13,24, 4, 7,21,25, 2,16,19,17,12, 6, 9,14,23, 3, 8,22,26 )$
$13^{2}$ $432$ $13$ $( 1,16,20,17,11, 6,10,14,24, 3, 7,22,25)( 2,15,19,18,12, 5, 9,13,23, 4, 8,21, 26)$
$26$ $432$ $26$ $( 1,23,17,21,10,15, 3,12,25,13,20, 8, 6, 2,24,18,22, 9,16, 4,11,26,14,19, 7, 5 )$
$13^{2}$ $432$ $13$ $( 1,24,17,22,10,16, 3,11,25,14,20, 7, 6)( 2,23,18,21, 9,15, 4,12,26,13,19, 8, 5)$
$13^{2}$ $432$ $13$ $( 1,25,22, 7, 3,24,14,10, 6,11,17,20,16)( 2,26,21, 8, 4,23,13, 9, 5,12,18,19, 15)$
$26$ $432$ $26$ $( 1,26,22, 8, 3,23,14, 9, 6,12,17,19,16, 2,25,21, 7, 4,24,13,10, 5,11,18,20,15 )$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $11232=2^{5} \cdot 3^{3} \cdot 13$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  11232.a
magma: IdentifyGroup(G);
 
Character table:

Size
2 P
3 P
13 P
Type

magma: CharacterTable(G);