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Properties

Label 11T1
Degree $11$
Order $11$
Cyclic yes
Abelian yes
Solvable yes
Primitive yes
$p$-group yes
Group: $C_{11}$

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Show commands: Magma

magma: G := TransitiveGroup(11, 1);
 

Group action invariants

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

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $11$ (is prime)
magma: Order(G);
 
Cyclic:  yes
magma: IsCyclic(G);
 
Abelian:  yes
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:  $1$
Label:  11.1
magma: IdentifyGroup(G);
 
Character table:    
     11  1   1   1   1   1   1   1   1   1   1   1

        1a 11a 11b 11c 11d 11e 11f 11g 11h 11i 11j

X.1      1   1   1   1   1   1   1   1   1   1   1
X.2      1   A   B   C   D   E  /E  /D  /C  /B  /A
X.3      1   B   D  /E  /C  /A   A   C   E  /D  /B
X.4      1   C  /E  /B   A   D  /D  /A   B   E  /C
X.5      1   D  /C   A   E  /B   B  /E  /A   C  /D
X.6      1   E  /A   D  /B   C  /C   B  /D   A  /E
X.7      1  /E   A  /D   B  /C   C  /B   D  /A   E
X.8      1  /D   C  /A  /E   B  /B   E   A  /C   D
X.9      1  /C   E   B  /A  /D   D   A  /B  /E   C
X.10     1  /B  /D   E   C   A  /A  /C  /E   D   B
X.11     1  /A  /B  /C  /D  /E   E   D   C   B   A

A = E(11)
B = E(11)^2
C = E(11)^3
D = E(11)^4
E = E(11)^5

magma: CharacterTable(G);