Properties

Label 14T30
Degree $14$
Order $1092$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $\PSL(2,13)$

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Show commands: Magma

magma: G := TransitiveGroup(14, 30);
 

Group action invariants

Degree $n$:  $14$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $30$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $\PSL(2,13)$
CHM label:   $L(14)=PSL(2,13)$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,12)(2,6)(3,4)(7,11)(9,10)(13,14), (1,4,3,12,9,10)(2,8,6,11,5,7), (1,2,3,4,5,6,7,8,9,10,11,12,14)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 7: None

Low degree siblings

28T120, 42T176

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

LabelCycle TypeSizeOrderRepresentative
1A $1^{14}$ $1$ $1$ $()$
2A $2^{6},1^{2}$ $91$ $2$ $( 1, 3)( 2, 8)( 5,11)( 6, 7)(10,12)(13,14)$
3A $3^{4},1^{2}$ $182$ $3$ $( 1, 4, 2)( 5,14, 8)( 6, 7,13)( 9,12,11)$
6A $6^{2},1^{2}$ $182$ $6$ $( 1, 6,10, 3, 7,12)( 2, 5,14, 8,11,13)$
7A1 $7^{2}$ $156$ $7$ $( 1,12, 3, 5,14, 8,10)( 2, 7, 6,11, 4,13, 9)$
7A2 $7^{2}$ $156$ $7$ $( 1, 3,14,10,12, 5, 8)( 2, 6, 4, 9, 7,11,13)$
7A3 $7^{2}$ $156$ $7$ $( 1, 5,10, 3, 8,12,14)( 2,11, 9, 6,13, 7, 4)$
13A1 $13,1$ $84$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,14, 8, 3,11, 6)$
13A2 $13,1$ $84$ $13$ $( 1, 4, 7,10,14, 3, 6, 9,12, 2, 5, 8,11)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $1092=2^{2} \cdot 3 \cdot 7 \cdot 13$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  1092.25
magma: IdentifyGroup(G);
 
Character table:

1A 2A 3A 6A 7A1 7A2 7A3 13A1 13A2
Size 1 91 182 182 156 156 156 84 84
2 P 1A 1A 3A 3A 7A2 7A3 7A1 13A2 13A1
3 P 1A 2A 1A 2A 7A3 7A1 7A2 13A1 13A2
7 P 1A 2A 3A 6A 1A 1A 1A 13A2 13A1
13 P 1A 2A 3A 6A 7A1 7A2 7A3 1A 1A
Type
1092.25.1a R 1 1 1 1 1 1 1 1 1
1092.25.7a1 R 7 1 1 1 0 0 0 ζ136+ζ135+ζ132+1+ζ132+ζ135+ζ136 ζ136ζ135ζ132ζ132ζ135ζ136
1092.25.7a2 R 7 1 1 1 0 0 0 ζ136ζ135ζ132ζ132ζ135ζ136 ζ136+ζ135+ζ132+1+ζ132+ζ135+ζ136
1092.25.12a1 R 12 0 0 0 ζ71ζ7 ζ72ζ72 ζ73ζ73 1 1
1092.25.12a2 R 12 0 0 0 ζ72ζ72 ζ73ζ73 ζ71ζ7 1 1
1092.25.12a3 R 12 0 0 0 ζ73ζ73 ζ71ζ7 ζ72ζ72 1 1
1092.25.13a R 13 1 1 1 1 1 1 0 0
1092.25.14a R 14 2 1 1 0 0 0 1 1
1092.25.14b R 14 2 1 1 0 0 0 1 1

magma: CharacterTable(G);