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Properties

Label 22T9
Degree $22$
Order $484$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{11}^2$

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Show commands: Magma

magma: G := TransitiveGroup(22, 9);
 

Group action invariants

Degree $n$:  $22$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $D_{11}^2$
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:  (1,5)(2,4)(6,11)(7,10)(8,9)(13,22)(14,21)(15,20)(16,19)(17,18), (1,13,2,18,3,12,4,17,5,22,6,16,7,21,8,15,9,20,10,14,11,19)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$22$:  $D_{11}$ x 2
$44$:  $D_{22}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T9 x 4, 44T29 x 5

Siblings are shown 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, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $4$ $11$ $(12,17,22,16,21,15,20,14,19,13,18)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $2$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11 $ $2$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,18,13,19,14,20,15,21,16,22,17)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,19,15,22,18,14,21,17,13,20,16)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,21,19,17,15,13,22,20,18,16,14)$
$ 11, 11 $ $4$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11 $ $2$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,13,14,15,16,17,18,19,20,21,22)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,19,15,22,18,14,21,17,13,20,16)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $4$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,21,19,17,15,13,22,20,18,16,14)$
$ 11, 11 $ $2$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11 $ $4$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $4$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $2$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16,20,13,17,21,14,18,22,15,19)$
$ 11, 11 $ $2$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,19,15,22,18,14,21,17,13,20,16)$
$ 11, 11 $ $4$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $4$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,21,19,17,15,13,22,20,18,16,14)$
$ 11, 11 $ $2$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11 $ $4$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $4$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11 $ $2$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14)$
$ 11, 11 $ $2$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20)$
$ 11, 11 $ $2$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,20,17,14,22,19,16,13,21,18,15)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $11$ $2$ $( 1,12)( 2,17)( 3,22)( 4,16)( 5,21)( 6,15)( 7,20)( 8,14)( 9,19)(10,13)(11,18)$
$ 22 $ $22$ $22$ $( 1,12, 2,17, 3,22, 4,16, 5,21, 6,15, 7,20, 8,14, 9,19,10,13,11,18)$
$ 22 $ $22$ $22$ $( 1,12, 3,22, 5,21, 7,20, 9,19,11,18, 2,17, 4,16, 6,15, 8,14,10,13)$
$ 22 $ $22$ $22$ $( 1,12, 4,16, 7,20,10,13, 2,17, 5,21, 8,14,11,18, 3,22, 6,15, 9,19)$
$ 22 $ $22$ $22$ $( 1,12, 5,21, 9,19, 2,17, 6,15,10,13, 3,22, 7,20,11,18, 4,16, 8,14)$
$ 22 $ $22$ $22$ $( 1,12, 6,15,11,18, 5,21,10,13, 4,16, 9,19, 3,22, 8,14, 2,17, 7,20)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ $11$ $2$ $( 1,12)( 2,18)( 3,13)( 4,19)( 5,14)( 6,20)( 7,15)( 8,21)( 9,16)(10,22)(11,17)$
$ 22 $ $22$ $22$ $( 1,12, 2,18, 3,13, 4,19, 5,14, 6,20, 7,15, 8,21, 9,16,10,22,11,17)$
$ 22 $ $22$ $22$ $( 1,12, 3,13, 5,14, 7,15, 9,16,11,17, 2,18, 4,19, 6,20, 8,21,10,22)$
$ 22 $ $22$ $22$ $( 1,12, 4,19, 7,15,10,22, 2,18, 5,14, 8,21,11,17, 3,13, 6,20, 9,16)$
$ 22 $ $22$ $22$ $( 1,12, 5,14, 9,16, 2,18, 6,20,10,22, 3,13, 7,15,11,17, 4,19, 8,21)$
$ 22 $ $22$ $22$ $( 1,12, 6,20,11,17, 5,14,10,22, 4,19, 9,16, 3,13, 8,21, 2,18, 7,15)$

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $484=2^{2} \cdot 11^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  484.9
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);