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Properties

Label 44T11
44T11 1 11 1->11 13 1->13 2 9 2->9 14 2->14 3 10 3->10 15 3->15 4 12 4->12 16 4->16 5 5->13 20 5->20 6 6->15 19 6->19 7 7->16 18 7->18 8 8->14 17 8->17 9->18 21 9->21 10->20 22 10->22 11->19 23 11->23 12->17 24 12->24 13->21 28 13->28 14->23 27 14->27 15->24 26 15->26 16->22 25 16->25 17->25 32 17->32 18->27 31 18->31 19->28 30 19->30 20->26 29 20->29 21->29 36 21->36 22->31 35 22->35 23->32 34 23->34 24->30 33 24->33 25->33 38 25->38 26->35 37 26->37 27->36 40 27->40 28->34 39 28->39 29->39 41 29->41 30->37 42 30->42 31->38 43 31->43 32->40 44 32->44 33->4 33->44 34->3 34->42 35->2 35->41 36->1 36->43 37->4 37->8 38->2 38->7 39->1 39->6 40->3 40->5 41->8 41->11 42->6 42->12 43->5 43->9 44->7 44->10
Degree $44$
Order $132$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}\times A_4$

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Copy content magma:G := TransitiveGroup(44, 11);
 

Group invariants

Abstract group:  $C_{11}\times A_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $132=2^{2} \cdot 3 \cdot 11$
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 $n$:  $44$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $11$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $11$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,13,28,39,6,19,30,42,12,24,33,4,16,25,38,7,18,31,43,9,21,36)(2,14,27,40,5,20,29,41,11,23,34,3,15,26,37,8,17,32,44,10,22,35)$, $(1,11,19,28,34,42,6,15,24,30,37,4,12,17,25,33,44,7,16,22,31,38,2,9,18,27,36,43,5,13,21,29,39)(3,10,20,26,35,41,8,14,23,32,40)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$3$:  $C_3$
$11$:  $C_{11}$
$12$:  $A_4$
$33$:  $C_{33}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: $A_4$

Degree 11: $C_{11}$

Degree 22: 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

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{44}$ $1$ $1$ $0$ $()$
2A $2^{22}$ $3$ $2$ $22$ $( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)$
3A1 $3^{11},1^{11}$ $4$ $3$ $22$ $( 2, 4, 3)( 5, 7, 8)( 9,10,11)(13,14,15)(17,19,20)(22,24,23)(25,26,27)(29,31,32)(34,36,35)(37,39,40)(41,44,42)$
3A-1 $3^{11},1^{11}$ $4$ $3$ $22$ $( 2, 3, 4)( 5, 8, 7)( 9,11,10)(13,15,14)(17,20,19)(22,23,24)(25,27,26)(29,32,31)(34,35,36)(37,40,39)(41,42,44)$
11A1 $11^{4}$ $1$ $11$ $40$ $( 1,12,18,28,33,43, 6,16,21,30,38)( 2,11,17,27,34,44, 5,15,22,29,37)( 3,10,20,26,35,41, 8,14,23,32,40)( 4, 9,19,25,36,42, 7,13,24,31,39)$
11A-1 $11^{4}$ $1$ $11$ $40$ $( 1,38,30,21,16, 6,43,33,28,18,12)( 2,37,29,22,15, 5,44,34,27,17,11)( 3,40,32,23,14, 8,41,35,26,20,10)( 4,39,31,24,13, 7,42,36,25,19, 9)$
11A2 $11^{4}$ $1$ $11$ $40$ $( 1,18,33, 6,21,38,12,28,43,16,30)( 2,17,34, 5,22,37,11,27,44,15,29)( 3,20,35, 8,23,40,10,26,41,14,32)( 4,19,36, 7,24,39, 9,25,42,13,31)$
11A-2 $11^{4}$ $1$ $11$ $40$ $( 1,30,16,43,28,12,38,21, 6,33,18)( 2,29,15,44,27,11,37,22, 5,34,17)( 3,32,14,41,26,10,40,23, 8,35,20)( 4,31,13,42,25, 9,39,24, 7,36,19)$
11A3 $11^{4}$ $1$ $11$ $40$ $( 1,28, 6,30,12,33,16,38,18,43,21)( 2,27, 5,29,11,34,15,37,17,44,22)( 3,26, 8,32,10,35,14,40,20,41,23)( 4,25, 7,31, 9,36,13,39,19,42,24)$
11A-3 $11^{4}$ $1$ $11$ $40$ $( 1,21,43,18,38,16,33,12,30, 6,28)( 2,22,44,17,37,15,34,11,29, 5,27)( 3,23,41,20,40,14,35,10,32, 8,26)( 4,24,42,19,39,13,36, 9,31, 7,25)$
11A4 $11^{4}$ $1$ $11$ $40$ $( 1,33,21,12,43,30,18, 6,38,28,16)( 2,34,22,11,44,29,17, 5,37,27,15)( 3,35,23,10,41,32,20, 8,40,26,14)( 4,36,24, 9,42,31,19, 7,39,25,13)$
11A-4 $11^{4}$ $1$ $11$ $40$ $( 1,16,28,38, 6,18,30,43,12,21,33)( 2,15,27,37, 5,17,29,44,11,22,34)( 3,14,26,40, 8,20,32,41,10,23,35)( 4,13,25,39, 7,19,31,42, 9,24,36)$
11A5 $11^{4}$ $1$ $11$ $40$ $( 1,43,38,33,30,28,21,18,16,12, 6)( 2,44,37,34,29,27,22,17,15,11, 5)( 3,41,40,35,32,26,23,20,14,10, 8)( 4,42,39,36,31,25,24,19,13, 9, 7)$
11A-5 $11^{4}$ $1$ $11$ $40$ $( 1, 6,12,16,18,21,28,30,33,38,43)( 2, 5,11,15,17,22,27,29,34,37,44)( 3, 8,10,14,20,23,26,32,35,40,41)( 4, 7, 9,13,19,24,25,31,36,39,42)$
22A1 $22^{2}$ $3$ $22$ $42$ $( 1, 5,12,15,18,22,28,29,33,37,43, 2, 6,11,16,17,21,27,30,34,38,44)( 3, 7,10,13,20,24,26,31,35,39,41, 4, 8, 9,14,19,23,25,32,36,40,42)$
22A-1 $22^{2}$ $3$ $22$ $42$ $( 1,42,38,36,30,25,21,19,16, 9, 6, 4,43,39,33,31,28,24,18,13,12, 7)( 2,41,37,35,29,26,22,20,15,10, 5, 3,44,40,34,32,27,23,17,14,11, 8)$
22A3 $22^{2}$ $3$ $22$ $42$ $( 1,15,28,37, 6,17,30,44,12,22,33, 2,16,27,38, 5,18,29,43,11,21,34)( 3,13,26,39, 8,19,32,42,10,24,35, 4,14,25,40, 7,20,31,41, 9,23,36)$
22A-3 $22^{2}$ $3$ $22$ $42$ $( 1,36,21, 9,43,31,18, 7,38,25,16, 4,33,24,12,42,30,19, 6,39,28,13)( 2,35,22,10,44,32,17, 8,37,26,15, 3,34,23,11,41,29,20, 5,40,27,14)$
22A5 $22^{2}$ $3$ $22$ $42$ $( 1,22,43,17,38,15,33,11,30, 5,28, 2,21,44,18,37,16,34,12,29, 6,27)( 3,24,41,19,40,13,35, 9,32, 7,26, 4,23,42,20,39,14,36,10,31, 8,25)$
22A-5 $22^{2}$ $3$ $22$ $42$ $( 1,25, 6,31,12,36,16,39,18,42,21, 4,28, 7,30, 9,33,13,38,19,43,24)( 2,26, 5,32,11,35,15,40,17,41,22, 3,27, 8,29,10,34,14,37,20,44,23)$
22A7 $22^{2}$ $3$ $22$ $42$ $( 1,29,16,44,28,11,38,22, 6,34,18, 2,30,15,43,27,12,37,21, 5,33,17)( 3,31,14,42,26, 9,40,24, 8,36,20, 4,32,13,41,25,10,39,23, 7,35,19)$
22A-7 $22^{2}$ $3$ $22$ $42$ $( 1,19,33, 7,21,39,12,25,43,13,30, 4,18,36, 6,24,38, 9,28,42,16,31)( 2,20,34, 8,22,40,11,26,44,14,29, 3,17,35, 5,23,37,10,27,41,15,32)$
22A9 $22^{2}$ $3$ $22$ $42$ $( 1,37,30,22,16, 5,43,34,28,17,12, 2,38,29,21,15, 6,44,33,27,18,11)( 3,39,32,24,14, 7,41,36,26,19,10, 4,40,31,23,13, 8,42,35,25,20, 9)$
22A-9 $22^{2}$ $3$ $22$ $42$ $( 1, 9,18,25,33,42, 6,13,21,31,38, 4,12,19,28,36,43, 7,16,24,30,39)( 2,10,17,26,34,41, 5,14,22,32,37, 3,11,20,27,35,44, 8,15,23,29,40)$
33A1 $33,11$ $4$ $33$ $42$ $( 1,12,18,28,33,43, 6,16,21,30,38)( 2,10,19,27,35,42, 5,14,24,29,40, 4,11,20,25,34,41, 7,15,23,31,37, 3, 9,17,26,36,44, 8,13,22,32,39)$
33A-1 $33,11$ $4$ $33$ $42$ $( 1,38,30,21,16, 6,43,33,28,18,12)( 2,39,32,22,13, 8,44,36,26,17, 9, 3,37,31,23,15, 7,41,34,25,20,11, 4,40,29,24,14, 5,42,35,27,19,10)$
33A2 $33,11$ $4$ $33$ $42$ $( 1,18,33, 6,21,38,12,28,43,16,30)( 2,19,35, 5,24,40,11,25,41,15,31, 3,17,36, 8,22,39,10,27,42,14,29, 4,20,34, 7,23,37, 9,26,44,13,32)$
33A-2 $33,11$ $4$ $33$ $42$ $( 1,30,16,43,28,12,38,21, 6,33,18)( 2,32,13,44,26, 9,37,23, 7,34,20, 4,29,14,42,27,10,39,22, 8,36,17, 3,31,15,41,25,11,40,24, 5,35,19)$
33A4 $33,11$ $4$ $33$ $42$ $( 1,33,21,12,43,30,18, 6,38,28,16)( 2,35,24,11,41,31,17, 8,39,27,14, 4,34,23, 9,44,32,19, 5,40,25,15, 3,36,22,10,42,29,20, 7,37,26,13)$
33A-4 $33,11$ $4$ $33$ $42$ $( 1,16,28,38, 6,18,30,43,12,21,33)( 2,13,26,37, 7,20,29,42,10,22,36, 3,15,25,40, 5,19,32,44, 9,23,34, 4,14,27,39, 8,17,31,41,11,24,35)$
33A5 $33,11$ $4$ $33$ $42$ $( 1,43,38,33,30,28,21,18,16,12, 6)( 2,42,40,34,31,26,22,19,14,11, 7, 3,44,39,35,29,25,23,17,13,10, 5, 4,41,37,36,32,27,24,20,15, 9, 8)$
33A-5 $33,11$ $4$ $33$ $42$ $( 1, 5, 9,16,17,24,28,29,36,38,44, 4, 6,11,13,18,22,25,30,34,39,43, 2, 7,12,15,19,21,27,31,33,37,42)( 3, 8,10,14,20,23,26,32,35,40,41)$
33A7 $33,11$ $4$ $33$ $42$ $( 1,16,28,38, 6,18,30,43,12,21,33)( 2,14,25,37, 8,19,29,41, 9,22,35, 4,15,26,39, 5,20,31,44,10,24,34, 3,13,27,40, 7,17,32,42,11,23,36)$
33A-7 $33,11$ $4$ $33$ $42$ $( 1,33,21,12,43,30,18, 6,38,28,16)( 2,36,23,11,42,32,17, 7,40,27,13, 3,34,24,10,44,31,20, 5,39,26,15, 4,35,22, 9,41,29,19, 8,37,25,14)$
33A8 $33,11$ $4$ $33$ $42$ $( 1,21,43,18,38,16,33,12,30, 6,28)( 2,24,41,17,39,14,34, 9,32, 5,25, 3,22,42,20,37,13,35,11,31, 8,27, 4,23,44,19,40,15,36,10,29, 7,26)$
33A-8 $33,11$ $4$ $33$ $42$ $( 1,28, 6,30,12,33,16,38,18,43,21)( 2,26, 7,29,10,36,15,40,19,44,23, 4,27, 8,31,11,35,13,37,20,42,22, 3,25, 5,32, 9,34,14,39,17,41,24)$
33A10 $33,11$ $4$ $33$ $42$ $( 1,38,30,21,16, 6,43,33,28,18,12)( 2,40,31,22,14, 7,44,35,25,17,10, 4,37,32,24,15, 8,42,34,26,19,11, 3,39,29,23,13, 5,41,36,27,20, 9)$
33A-10 $33,11$ $4$ $33$ $42$ $( 1,12,18,28,33,43, 6,16,21,30,38)( 2, 9,20,27,36,41, 5,13,23,29,39, 3,11,19,26,34,42, 8,15,24,32,37, 4,10,17,25,35,44, 7,14,22,31,40)$
33A13 $33,11$ $4$ $33$ $42$ $( 1,18,33, 6,21,38,12,28,43,16,30)( 2,20,36, 5,23,39,11,26,42,15,32, 4,17,35, 7,22,40, 9,27,41,13,29, 3,19,34, 8,24,37,10,25,44,14,31)$
33A-13 $33,11$ $4$ $33$ $42$ $( 1,30,16,43,28,12,38,21, 6,33,18)( 2,31,14,44,25,10,37,24, 8,34,19, 3,29,13,41,27, 9,40,22, 7,35,17, 4,32,15,42,26,11,39,23, 5,36,20)$
33A14 $33,11$ $4$ $33$ $42$ $( 1,28, 6,30,12,33,16,38,18,43,21)( 2,25, 8,29, 9,35,15,39,20,44,24, 3,27, 7,32,11,36,14,37,19,41,22, 4,26, 5,31,10,34,13,40,17,42,23)$
33A-14 $33,11$ $4$ $33$ $42$ $( 1,21,43,18,38,16,33,12,30, 6,28)( 2,23,42,17,40,13,34,10,31, 5,26, 4,22,41,19,37,14,36,11,32, 7,27, 3,24,44,20,39,15,35, 9,29, 8,25)$
33A16 $33,11$ $4$ $33$ $42$ $( 1,43,38,33,30,28,21,18,16,12, 6)( 2,41,39,34,32,25,22,20,13,11, 8, 4,44,40,36,29,26,24,17,14, 9, 5, 3,42,37,35,31,27,23,19,15,10, 7)$
33A-16 $33,11$ $4$ $33$ $42$ $( 1, 5,10,16,17,23,28,29,35,38,44, 3, 6,11,14,18,22,26,30,34,40,43, 2, 8,12,15,20,21,27,32,33,37,41)( 4, 7, 9,13,19,24,25,31,36,39,42)$

Malle's constant $a(G)$:     $1/22$

Copy content magma:ConjugacyClasses(G);
 

Character table

44 x 44 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed