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Properties

Label 39T43
Degree $39$
Order $5616$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $\PSL(3,3)$

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Show commands: Magma

magma: G := TransitiveGroup(39, 43);
 

Group action invariants

Degree $n$:  $39$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $43$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $\PSL(3,3)$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,8,18,13,5,20,37,36)(2,9,16,14,4,19,39,34)(3,7,17,15,6,21,38,35)(10,24,33,27)(11,23,32,26,12,22,31,25)(28,30), (1,37,25,7)(2,39,26,9,3,38,27,8)(4,13,22,35,30,19,33,18)(5,14,23,36,28,20,31,16)(6,15,24,34,29,21,32,17)(11,12)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

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

Low degree siblings

13T7 x 2, 26T39 x 2, 39T43

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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 13, 13, 13 $ $432$ $13$ $( 1,27,32,18, 7,24,37,10,30,34,19, 5,13)( 2,25,33,16, 8,23,38,11,28,36,20, 6, 15)( 3,26,31,17, 9,22,39,12,29,35,21, 4,14)$
$ 13, 13, 13 $ $432$ $13$ $( 1,30,18, 5,37,27,34, 7,13,10,32,19,24)( 2,28,16, 6,38,25,36, 8,15,11,33,20, 23)( 3,29,17, 4,39,26,35, 9,14,12,31,21,22)$
$ 13, 13, 13 $ $432$ $13$ $( 1,13, 5,19,34,30,10,37,24, 7,18,32,27)( 2,15, 6,20,36,28,11,38,23, 8,16,33, 25)( 3,14, 4,21,35,29,12,39,22, 9,17,31,26)$
$ 13, 13, 13 $ $432$ $13$ $( 1,24,19,32,10,13, 7,34,27,37, 5,18,30)( 2,23,20,33,11,15, 8,36,25,38, 6,16, 28)( 3,22,21,31,12,14, 9,35,26,39, 4,17,29)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1 $ $117$ $2$ $( 2, 3)( 4,26)( 5,27)( 6,25)( 7,29)( 8,28)( 9,30)(10,39)(11,37)(12,38)(14,15) (17,18)(23,24)(31,35)(32,34)(33,36)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 1 $ $702$ $4$ $( 1,13)( 2,15, 3,14)( 4,28,26, 8)( 5,29,27, 7)( 6,30,25, 9)(10,35,39,31) (11,36,37,33)(12,34,38,32)(16,22)(17,24,18,23)$
$ 8, 8, 8, 8, 4, 2, 1 $ $702$ $8$ $( 1,16,13,22)( 2,18,14,24, 3,17,15,23)( 4,11, 8,33,26,37,28,36) ( 5,10, 7,31,27,39,29,35)( 6,12, 9,32,25,38,30,34)(20,21)$
$ 8, 8, 8, 8, 4, 2, 1 $ $702$ $8$ $( 1,22,13,16)( 2,23,15,17, 3,24,14,18)( 4,36,28,37,26,33, 8,11) ( 5,35,29,39,27,31, 7,10)( 6,34,30,38,25,32, 9,12)(20,21)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1 $ $104$ $3$ $( 1, 4,30)( 2, 6,28)( 3, 5,29)( 7, 9, 8)(13,21,39)(14,20,37)(15,19,38) (16,17,18)(22,27,31)(23,26,33)(24,25,32)(34,36,35)$
$ 6, 6, 6, 6, 6, 3, 3, 2, 1 $ $936$ $6$ $( 1,38, 5,20,28,13)( 2,39, 4,19,29,14)( 3,37, 6,21,30,15)( 7,36,18, 8,35,17) ( 9,34,16)(10,12)(22,26,24,27,23,25)(31,33,32)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $624$ $3$ $( 1,19,26)( 2,21,25)( 3,20,27)( 4,38,33)( 5,37,31)( 6,39,32)( 7,34,18) ( 8,35,17)( 9,36,16)(10,11,12)(13,24,28)(14,22,29)(15,23,30)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $5616=2^{4} \cdot 3^{3} \cdot 13$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  5616.a
magma: IdentifyGroup(G);
 
Character table:

Size
2 P
3 P
13 P
Type

magma: CharacterTable(G);