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Properties

Label 11T5
Degree $11$
Order $660$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $\PSL(2,11)$

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Show commands: Magma

magma: G := TransitiveGroup(11, 5);
 

Group action invariants

Degree $n$:  $11$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $5$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $\PSL(2,11)$
CHM label:  $L(11)=PSL(2,11)(11)$
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:  (1,2,3,4,5,6,7,8,9,10,11), (2,10)(3,4)(5,9)(6,7)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

11T5, 12T179

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 2, 2, 2, 2, 1, 1, 1 $ $55$ $2$ $( 3, 4)( 5, 7)( 6, 9)( 8,11)$
$ 3, 3, 3, 1, 1 $ $110$ $3$ $( 3, 5, 8)( 4,11, 7)( 6, 9,10)$
$ 5, 5, 1 $ $132$ $5$ $( 2, 3, 6, 9, 4)( 5,10, 7, 8,11)$
$ 5, 5, 1 $ $132$ $5$ $( 2, 3,10, 9, 7)( 4, 5,11, 8, 6)$
$ 6, 3, 2 $ $110$ $6$ $( 1, 2)( 3, 4, 8, 7, 5,11)( 6, 9,10)$
$ 11 $ $60$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)$
$ 11 $ $60$ $11$ $( 1, 2, 3, 6,10, 7, 5, 9,11, 8, 4)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $660=2^{2} \cdot 3 \cdot 5 \cdot 11$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  660.13
magma: IdentifyGroup(G);
 
Character table:    
     2  2  2  1  .  .  1   .   .
     3  1  1  1  .  .  1   .   .
     5  1  .  .  1  1  .   .   .
    11  1  .  .  .  .  .   1   1

       1a 2a 3a 5a 5b 6a 11a 11b
    2P 1a 1a 3a 5b 5a 3a 11b 11a
    3P 1a 2a 1a 5b 5a 2a 11a 11b
    5P 1a 2a 3a 1a 1a 6a 11a 11b
    7P 1a 2a 3a 5b 5a 6a 11b 11a
   11P 1a 2a 3a 5a 5b 6a  1a  1a

X.1     1  1  1  1  1  1   1   1
X.2     5  1 -1  .  .  1   B  /B
X.3     5  1 -1  .  .  1  /B   B
X.4    10 -2  1  .  .  1  -1  -1
X.5    10  2  1  .  . -1  -1  -1
X.6    11 -1 -1  1  1 -1   .   .
X.7    12  .  .  A *A  .   1   1
X.8    12  .  . *A  A  .   1   1

A = E(5)^2+E(5)^3
  = (-1-Sqrt(5))/2 = -1-b5
B = E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9
  = (-1+Sqrt(-11))/2 = b11

magma: CharacterTable(G);