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Properties

Label 22T8
22T8 1 8 1->8 21 1->21 2 7 2->7 16 2->16 3 6 3->6 22 3->22 4 5 4->5 17 4->17 12 5->12 18 6->18 13 7->13 19 8->19 9 11 9->11 14 9->14 10 20 10->20 15 11->15 12->7 12->19 13->5 13->18 14->3 14->17 15->1 15->16 16->10 17->8 19->4 20->2 20->22 21->11 22->9
Degree $22$
Order $484$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^2:C_4$

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Copy content magma:G := TransitiveGroup(22, 8);
 

Group invariants

Abstract group:  $C_{11}^2:C_4$
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 $t$:  $8$
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:  $(1,8)(2,7)(3,6)(4,5)(9,11)(12,19)(13,18)(14,17)(15,16)(20,22)$, $(1,21,11,15)(2,16,10,20)(3,22,9,14)(4,17,8,19)(5,12,7,13)(6,18)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T8 x 5, 44T28 x 6

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

Malle's constant $a(G)$:     $1/10$

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Character table

34 x 34 character table

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Regular extensions

Data not computed