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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
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 13, 1 $ $84$ $13$ $( 1, 5,11, 8, 2,10,13, 4,12, 6, 3, 9,14)$
$ 13, 1 $ $84$ $13$ $( 1,12, 8, 9,13, 5, 6, 2,14, 4,11, 3,10)$
$ 2, 2, 2, 2, 2, 2, 1, 1 $ $91$ $2$ $( 2, 4)( 3,10)( 5,13)( 6, 8)( 7,14)(11,12)$
$ 3, 3, 3, 3, 1, 1 $ $182$ $3$ $( 2, 6,12)( 3, 5, 7)( 4, 8,11)(10,13,14)$
$ 6, 6, 1, 1 $ $182$ $6$ $( 2,11, 6, 4,12, 8)( 3,14, 5,10, 7,13)$
$ 7, 7 $ $156$ $7$ $( 1, 7, 9,13, 2, 4,10)( 3,14, 5,12, 6,11, 8)$
$ 7, 7 $ $156$ $7$ $( 1, 2, 7, 4, 9,10,13)( 3, 6,14,11, 5, 8,12)$
$ 7, 7 $ $156$ $7$ $( 1, 9, 2,10, 7,13, 4)( 3, 5, 6, 8,14,12,11)$

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 ζ13−6+ζ13−5+ζ13−2+1+ζ132+ζ135+ζ136 −ζ13−6−ζ13−5−ζ13−2−ζ132−ζ135−ζ136
1092.25.7a2 R 7 −1 1 −1 0 0 0 −ζ13−6−ζ13−5−ζ13−2−ζ132−ζ135−ζ136 ζ13−6+ζ13−5+ζ13−2+1+ζ132+ζ135+ζ136
1092.25.12a1 R 12 0 0 0 −ζ7−1−ζ7 −ζ7−2−ζ72 −ζ7−3−ζ73 −1 −1
1092.25.12a2 R 12 0 0 0 −ζ7−2−ζ72 −ζ7−3−ζ73 −ζ7−1−ζ7 −1 −1
1092.25.12a3 R 12 0 0 0 −ζ7−3−ζ73 −ζ7−1−ζ7 −ζ7−2−ζ72 −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);