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Properties

Label 22T9
22T9 1 5 1->5 13 1->13 2 4 2->4 18 2->18 3 12 3->12 17 4->17 22 5->22 6 11 6->11 16 6->16 7 10 7->10 21 7->21 8 9 8->9 15 8->15 20 9->20 14 10->14 19 11->19 12->4 13->2 13->22 14->11 14->21 15->9 15->20 16->7 16->19 17->5 17->18 18->3 19->1 20->10 21->8 22->6
Degree $22$
Order $484$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{11}^2$

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Copy content magma:G := TransitiveGroup(22, 9);
 

Group invariants

Abstract group:  $D_{11}^2$
Copy content magma:IdentifyGroup(G);
 
Order:  $484=2^{2} \cdot 11^{2}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $22$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,5)(2,4)(6,11)(7,10)(8,9)(13,22)(14,21)(15,20)(16,19)(17,18)$, $(1,13,2,18,3,12,4,17,5,22,6,16,7,21,8,15,9,20,10,14,11,19)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$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

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{22}$ $1$ $1$ $0$ $()$
2A $2^{11}$ $11$ $2$ $11$ $( 1,13)( 2,18)( 3,12)( 4,17)( 5,22)( 6,16)( 7,21)( 8,15)( 9,20)(10,14)(11,19)$
2B $2^{11}$ $11$ $2$ $11$ $( 1,22)( 2,17)( 3,12)( 4,18)( 5,13)( 6,19)( 7,14)( 8,20)( 9,15)(10,21)(11,16)$
2C $2^{10},1^{2}$ $121$ $2$ $10$ $( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,18)(13,17)(14,16)(19,22)(20,21)$
11A1 $11^{2}$ $2$ $11$ $20$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14)$
11A2 $11^{2}$ $2$ $11$ $20$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16)$
11A3 $11^{2}$ $2$ $11$ $20$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)$
11A4 $11^{2}$ $2$ $11$ $20$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20)$
11A5 $11^{2}$ $2$ $11$ $20$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,13,14,15,16,17,18,19,20,21,22)$
11B1 $11^{2}$ $2$ $11$ $20$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,22,21,20,19,18,17,16,15,14,13)$
11B2 $11^{2}$ $2$ $11$ $20$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,21,19,17,15,13,22,20,18,16,14)$
11B3 $11^{2}$ $2$ $11$ $20$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,20,17,14,22,19,16,13,21,18,15)$
11B4 $11^{2}$ $2$ $11$ $20$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,19,15,22,18,14,21,17,13,20,16)$
11B5 $11^{2}$ $2$ $11$ $20$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,18,13,19,14,20,15,21,16,22,17)$
11C1 $11^{2}$ $4$ $11$ $20$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,15,18,21,13,16,19,22,14,17,20)$
11C2 $11^{2}$ $4$ $11$ $20$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,18,13,19,14,20,15,21,16,22,17)$
11C3 $11^{2}$ $4$ $11$ $20$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,21,19,17,15,13,22,20,18,16,14)$
11C4 $11^{2}$ $4$ $11$ $20$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,13,14,15,16,17,18,19,20,21,22)$
11C5 $11^{2}$ $4$ $11$ $20$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,16,20,13,17,21,14,18,22,15,19)$
11D1 $11^{2}$ $4$ $11$ $20$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,20,17,14,22,19,16,13,21,18,15)$
11D2 $11^{2}$ $4$ $11$ $20$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,17,22,16,21,15,20,14,19,13,18)$
11D3 $11^{2}$ $4$ $11$ $20$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,20,17,14,22,19,16,13,21,18,15)$
11D4 $11^{2}$ $4$ $11$ $20$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,19,15,22,18,14,21,17,13,20,16)$
11D5 $11^{2}$ $4$ $11$ $20$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,18,13,19,14,20,15,21,16,22,17)$
11E1 $11^{2}$ $4$ $11$ $20$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,13,14,15,16,17,18,19,20,21,22)$
11E2 $11^{2}$ $4$ $11$ $20$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,14,16,18,20,22,13,15,17,19,21)$
11E3 $11^{2}$ $4$ $11$ $20$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,17,22,16,21,15,20,14,19,13,18)$
11E4 $11^{2}$ $4$ $11$ $20$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,15,18,21,13,16,19,22,14,17,20)$
11E5 $11^{2}$ $4$ $11$ $20$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,13,14,15,16,17,18,19,20,21,22)$
11F1 $11^{2}$ $4$ $11$ $20$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,14,16,18,20,22,13,15,17,19,21)$
11F2 $11^{2}$ $4$ $11$ $20$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,22,21,20,19,18,17,16,15,14,13)$
11F3 $11^{2}$ $4$ $11$ $20$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,16,20,13,17,21,14,18,22,15,19)$
11F4 $11^{2}$ $4$ $11$ $20$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,20,17,14,22,19,16,13,21,18,15)$
11F5 $11^{2}$ $4$ $11$ $20$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,22,21,20,19,18,17,16,15,14,13)$
11G1 $11,1^{11}$ $4$ $11$ $10$ $(12,22,21,20,19,18,17,16,15,14,13)$
11G2 $11,1^{11}$ $4$ $11$ $10$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)$
11G3 $11,1^{11}$ $4$ $11$ $10$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)$
11G4 $11,1^{11}$ $4$ $11$ $10$ $(12,19,15,22,18,14,21,17,13,20,16)$
11G5 $11,1^{11}$ $4$ $11$ $10$ $(12,18,13,19,14,20,15,21,16,22,17)$
22A1 $22$ $22$ $22$ $21$ $( 1,12, 5,21, 9,19, 2,17, 6,15,10,13, 3,22, 7,20,11,18, 4,16, 8,14)$
22A3 $22$ $22$ $22$ $21$ $( 1,21, 2,15, 3,20, 4,14, 5,19, 6,13, 7,18, 8,12, 9,17,10,22,11,16)$
22A5 $22$ $22$ $22$ $21$ $( 1,19,10,20, 8,21, 6,22, 4,12, 2,13,11,14, 9,15, 7,16, 5,17, 3,18)$
22A7 $22$ $22$ $22$ $21$ $( 1,17, 7,14, 2,22, 8,19, 3,16, 9,13, 4,21,10,18, 5,15,11,12, 6,20)$
22A9 $22$ $22$ $22$ $21$ $( 1,15, 4,19, 7,12,10,16, 2,20, 5,13, 8,17,11,21, 3,14, 6,18, 9,22)$
22B1 $22$ $22$ $22$ $21$ $( 1,16,10,15, 8,14, 6,13, 4,12, 2,22,11,21, 9,20, 7,19, 5,18, 3,17)$
22B3 $22$ $22$ $22$ $21$ $( 1,15, 6,12,11,20, 5,17,10,14, 4,22, 9,19, 3,16, 8,13, 2,21, 7,18)$
22B5 $22$ $22$ $22$ $21$ $( 1,14, 2,20, 3,15, 4,21, 5,16, 6,22, 7,17, 8,12, 9,18,10,13,11,19)$
22B7 $22$ $22$ $22$ $21$ $( 1,20, 4,16, 7,12,10,19, 2,15, 5,22, 8,18,11,14, 3,21, 6,17, 9,13)$
22B9 $22$ $22$ $22$ $21$ $( 1,21, 8,19, 4,17,11,15, 7,13, 3,22,10,20, 6,18, 2,16, 9,14, 5,12)$

Malle's constant $a(G)$:     $1/10$

Copy content magma:ConjugacyClasses(G);
 

Character table

49 x 49 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed