Properties

Label 46T17
46T17 1 26 1->26 39 1->39 2 25 2->25 2->39 3 29 3->29 34 3->34 4 42 4->42 43 4->43 5 5->29 32 5->32 6 38 6->38 45 6->45 7 24 7->24 35 7->35 8 8->25 33 8->33 9 9->38 9->42 10 28 10->28 10->28 11 37 11->37 41 11->41 12 31 12->31 46 12->46 13 13->32 44 13->44 14 14->34 14->41 15 15->24 27 15->27 16 36 16->36 16->37 17 17->27 17->45 18 18->31 40 18->40 19 30 19->30 19->40 20 20->26 20->43 21 21->33 21->35 22 22->44 22->46 23 23->30 23->36 24->12 24->23 25->18 25->19 26->3 26->13 27->8 27->10 28->3 28->17 29->1 29->21 30->8 30->16 31->11 31->15 32->6 32->22 33->1 33->6 34->13 34->19 35->14 35->20 36->4 36->9 37->4 37->11 38->18 38->22 39->17 40->9 40->12 41->7 41->16 42->2 42->23 43->7 43->20 44->14 44->15 45->10 45->21 46->5 46->5
Degree $46$
Order $46552$
Cyclic no
Abelian no
Solvable yes
Transitivity $1$
Primitive no
$p$-group no
Group: $D_{23}^2:D_{11}$

Related objects

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Copy content comment:Define the Galois group
 
Copy content magma:G := TransitiveGroup(46, 17);
 
Copy content sage:G = TransitiveGroup(46, 17)
 
Copy content oscar:G = transitive_group(46, 17)
 
Copy content gap:G := TransitiveGroup(46, 17);
 

Group invariants

Abstract group:  $D_{23}^2:D_{11}$
Copy content comment:Abstract group ID
 
Copy content magma:IdentifyGroup(G);
 
Copy content sage:G.id()
 
Copy content oscar:small_group_identification(G)
 
Copy content gap:IdGroup(G);
 
Order:  $46552=2^{3} \cdot 11 \cdot 23^{2}$
Copy content comment:Order
 
Copy content magma:Order(G);
 
Copy content sage:G.order()
 
Copy content oscar:order(G)
 
Copy content gap:Order(G);
 
Cyclic:  no
Copy content comment:Determine if group is cyclic
 
Copy content magma:IsCyclic(G);
 
Copy content sage:G.is_cyclic()
 
Copy content oscar:is_cyclic(G)
 
Copy content gap:IsCyclic(G);
 
Abelian:  no
Copy content comment:Determine if group is abelian
 
Copy content magma:IsAbelian(G);
 
Copy content sage:G.is_abelian()
 
Copy content oscar:is_abelian(G)
 
Copy content gap:IsAbelian(G);
 
Solvable:  yes
Copy content comment:Determine if group is solvable
 
Copy content magma:IsSolvable(G);
 
Copy content sage:G.is_solvable()
 
Copy content oscar:is_solvable(G)
 
Copy content gap:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content comment:Nilpotency class
 
Copy content magma:NilpotencyClass(G);
 
Copy content sage:libgap(G).NilpotencyClassOfGroup() if G.is_nilpotent() else -1
 
Copy content oscar:if is_nilpotent(G) nilpotency_class(G) end
 
Copy content gap:if IsNilpotentGroup(G) then NilpotencyClassOfGroup(G); fi;
 

Group action invariants

Degree $n$:  $46$
Copy content comment:Degree
 
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Copy content sage:G.degree()
 
Copy content oscar:degree(G)
 
Copy content gap:NrMovedPoints(G);
 
Transitive number $t$:  $17$
Copy content comment:Transitive number
 
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Copy content sage:G.transitive_number()
 
Copy content oscar:transitive_group_identification(G)[2]
 
Copy content gap:TransitiveIdentification(G);
 
Parity:  $-1$
Copy content comment:Parity
 
Copy content magma:IsEven(G);
 
Copy content sage:all(g.SignPerm() == 1 for g in libgap(G).GeneratorsOfGroup())
 
Copy content oscar:is_even(G)
 
Copy content gap:ForAll(GeneratorsOfGroup(G), g -> SignPerm(g) = 1);
 
Transitivity:  1
Primitive:  no
Copy content comment:Determine if group is primitive
 
Copy content magma:IsPrimitive(G);
 
Copy content sage:G.is_primitive()
 
Copy content oscar:is_primitive(G)
 
Copy content gap:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content comment:Order of the centralizer of G in S_n
 
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Copy content sage:SymmetricGroup(46).centralizer(G).order()
 
Copy content oscar:order(centralizer(symmetric_group(46), G)[1])
 
Copy content gap:Order(Centralizer(SymmetricGroup(46), G));
 
Generators:  $(1,39,17,45,10,28,3,34,19,40,12,46,5,29,21,35,14,41,7,24,23,30,16,36,9,42,2,25,18,31,11,37,4,43,20,26,13,32,6,38,22,44,15,27,8,33)$, $(1,26,3,29)(2,39)(4,42,23,36)(5,32,22,46)(6,45,21,33)(7,35,20,43)(8,25,19,30)(9,38,18,40)(10,28,17,27)(11,41,16,37)(12,31,15,24)(13,44,14,34)$
Copy content comment:Generators
 
Copy content magma:Generators(G);
 
Copy content sage:G.gens()
 
Copy content oscar:gens(G)
 
Copy content gap:GeneratorsOfGroup(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$
$22$:  $D_{11}$
$44$:  $D_{22}$
$88$:  44T6

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: 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 $1^{46}$ $1$ $1$ $0$ $()$
2A $2^{11},1^{24}$ $46$ $2$ $11$ $( 1,13)( 2,12)( 3,11)( 4,10)( 5, 9)( 6, 8)(14,23)(15,22)(16,21)(17,20)(18,19)$
2B $2^{23}$ $506$ $2$ $23$ $( 1,33)( 2,31)( 3,29)( 4,27)( 5,25)( 6,46)( 7,44)( 8,42)( 9,40)(10,38)(11,36)(12,34)(13,32)(14,30)(15,28)(16,26)(17,24)(18,45)(19,43)(20,41)(21,39)(22,37)(23,35)$
2C $2^{22},1^{2}$ $529$ $2$ $22$ $( 1,12)( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,23)(14,22)(15,21)(16,20)(17,19)(24,46)(25,45)(26,44)(27,43)(28,42)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)$
4A $4^{11},2$ $11638$ $4$ $34$ $( 1,43,12,27)( 2,29,11,41)( 3,38,10,32)( 4,24, 9,46)( 5,33, 8,37)( 6,42, 7,28)(13,36,23,34)(14,45,22,25)(15,31,21,39)(16,40,20,30)(17,26,19,44)(18,35)$
11A1 $11^{4},1^{2}$ $1058$ $11$ $40$ $( 1,14,18,21, 6,12, 5,17, 3, 4,22)( 2, 9,20,11,10,15,13,23,19,16, 8)(24,34,32,37,36,27,38,45,39,31,28)(25,43,44,30,42,35,41,26,29,33,46)$
11A2 $11^{4},1^{2}$ $1058$ $11$ $40$ $( 1,18, 6, 5, 3,22,14,21,12,17, 4)( 2,20,10,13,19, 8, 9,11,15,23,16)(24,32,36,38,39,28,34,37,27,45,31)(25,44,42,41,29,46,43,30,35,26,33)$
11A3 $11^{4},1^{2}$ $1058$ $11$ $40$ $( 1,21, 5, 4,14, 6,17,22,18,12, 3)( 2,11,13,16, 9,10,23, 8,20,15,19)(24,37,38,31,34,36,45,28,32,27,39)(25,30,41,33,43,42,26,46,44,35,29)$
11A4 $11^{4},1^{2}$ $1058$ $11$ $40$ $( 1, 6, 3,14,12, 4,18, 5,22,21,17)( 2,10,19, 9,15,16,20,13, 8,11,23)(24,36,39,34,27,31,32,38,28,37,45)(25,42,29,43,35,33,44,41,46,30,26)$
11A5 $11^{4},1^{2}$ $1058$ $11$ $40$ $( 1,12,22, 6, 4,21, 3,18,17,14, 5)( 2,15, 8,10,16,11,19,20,23, 9,13)(24,27,28,36,31,37,39,32,45,34,38)(25,35,46,42,33,30,29,44,26,43,41)$
22A1 $22^{2},1^{2}$ $1058$ $22$ $42$ $( 1,21,14,13, 3,18, 7,12,16,10,19,17,20, 4, 5,15,23,11, 6, 2, 8,22)(24,27,25,34,28,32,37,26,41,31,30,46,43,45,36,42,38,33,44,29,39,40)$
22A3 $22^{2},1^{2}$ $1058$ $22$ $42$ $( 1,13, 7,10,20,15, 6,22,14,18,16,17, 5,11, 8,21, 3,12,19, 4,23, 2)(24,34,37,31,43,42,44,40,25,32,41,46,36,33,39,27,28,26,30,45,38,29)$
22A5 $22^{2},1^{2}$ $1058$ $22$ $42$ $( 1,18,19,15, 8,13,16, 4, 6,21, 7,17,23,22, 3,10, 5, 2,14,12,20,11)(24,32,30,42,39,34,41,45,44,27,37,46,38,40,28,31,36,29,25,26,43,33)$
22A7 $22^{2},1^{2}$ $1058$ $22$ $42$ $( 1,12, 5,22, 7, 4, 8,18,20, 2, 3,17, 6,13,19,11,14,10,23,21,16,15)(24,26,36,40,37,45,39,32,43,29,28,46,44,34,30,33,25,31,38,27,41,42)$
22A9 $22^{2},1^{2}$ $1058$ $22$ $42$ $( 1,10, 6,18, 5,21,19, 2, 7,15,14,17, 8,12,23,13,20,22,16,11, 3, 4)(24,31,44,32,36,27,30,29,37,42,25,46,39,26,38,34,43,40,41,33,28,45)$
22B1 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1, 9,14,20,18,11,21,10, 6,15,12,13, 5,23,17,19, 3,16, 4, 8,22, 2)(24,38,34,45,32,39,37,31,36,28,27)(25,41,43,26,44,29,30,33,42,46,35)$
22B-1 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1, 2,22, 8, 4,16, 3,19,17,23, 5,13,12,15, 6,10,21,11,18,20,14, 9)(24,27,28,36,31,37,39,32,45,34,38)(25,35,46,42,33,30,29,44,26,43,41)$
22B3 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,20,21,15, 5,19, 4, 2,14,11, 6,13,17,16,22, 9,18,10,12,23, 3, 8)(24,45,37,28,38,32,31,27,34,39,36)(25,26,30,46,41,44,33,35,43,29,42)$
22B-3 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1, 8, 3,23,12,10,18, 9,22,16,17,13, 6,11,14, 2, 4,19, 5,15,21,20)(24,36,39,34,27,31,32,38,28,37,45)(25,42,29,43,35,33,44,41,46,30,26)$
22B5 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,11,12,19,22,20, 6,23, 4, 9,21,13, 3, 2,18,15,17, 8,14,10, 5,16)(24,39,27,32,28,45,36,34,31,38,37)(25,29,35,44,46,26,42,43,33,41,30)$
22B-5 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,16, 5,10,14, 8,17,15,18, 2, 3,13,21, 9, 4,23, 6,20,22,19,12,11)(24,37,38,31,34,36,45,28,32,27,39)(25,30,41,33,43,42,26,46,44,35,29)$
22B7 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,10,17, 2,21,23,22,11, 5, 8,18,13, 4,20,12,16,14,15, 3, 9, 6,19)(24,31,45,27,37,34,28,39,38,36,32)(25,33,26,35,30,43,46,29,41,42,44)$
22B-7 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,19, 6, 9, 3,15,14,16,12,20, 4,13,18, 8, 5,11,22,23,21, 2,17,10)(24,32,36,38,39,28,34,37,27,45,31)(25,44,42,41,29,46,43,30,35,26,33)$
22B9 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,15, 4,11,17, 9,12, 8,21,19,14,13,22,10, 3,20, 5, 2, 6,16,18,23)(24,28,31,39,45,38,27,36,37,32,34)(25,46,33,29,26,41,35,42,30,44,43)$
22B-9 $22,11^{2},1^{2}$ $1058$ $22$ $41$ $( 1,23,18,16, 6, 2, 5,20, 3,10,22,13,14,19,21, 8,12, 9,17,11, 4,15)(24,34,32,37,36,27,38,45,39,31,28)(25,43,44,30,42,35,41,26,29,33,46)$
23A $23,1^{23}$ $44$ $23$ $22$ $(24,45,43,41,39,37,35,33,31,29,27,25,46,44,42,40,38,36,34,32,30,28,26)$
23B1 $23^{2}$ $44$ $23$ $44$ $( 1,11,21, 8,18, 5,15, 2,12,22, 9,19, 6,16, 3,13,23,10,20, 7,17, 4,14)(24,27,30,33,36,39,42,45,25,28,31,34,37,40,43,46,26,29,32,35,38,41,44)$
23B2 $23^{2}$ $44$ $23$ $44$ $( 1,21,18,15,12, 9, 6, 3,23,20,17,14,11, 8, 5, 2,22,19,16,13,10, 7, 4)(24,30,36,42,25,31,37,43,26,32,38,44,27,33,39,45,28,34,40,46,29,35,41)$
23B3 $23^{2}$ $44$ $23$ $44$ $( 1, 8,15,22, 6,13,20, 4,11,18, 2, 9,16,23, 7,14,21, 5,12,19, 3,10,17)(24,33,42,28,37,46,32,41,27,36,45,31,40,26,35,44,30,39,25,34,43,29,38)$
23B4 $23^{2}$ $44$ $23$ $44$ $( 1,18,12, 6,23,17,11, 5,22,16,10, 4,21,15, 9, 3,20,14, 8, 2,19,13, 7)(24,36,25,37,26,38,27,39,28,40,29,41,30,42,31,43,32,44,33,45,34,46,35)$
23B5 $23^{2}$ $44$ $23$ $44$ $( 1, 5, 9,13,17,21, 2, 6,10,14,18,22, 3, 7,11,15,19,23, 4, 8,12,16,20)(24,39,31,46,38,30,45,37,29,44,36,28,43,35,27,42,34,26,41,33,25,40,32)$
23B6 $23^{2}$ $44$ $23$ $44$ $( 1,15, 6,20,11, 2,16, 7,21,12, 3,17, 8,22,13, 4,18, 9,23,14, 5,19,10)(24,42,37,32,27,45,40,35,30,25,43,38,33,28,46,41,36,31,26,44,39,34,29)$
23B7 $23^{2}$ $44$ $23$ $44$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,45,43,41,39,37,35,33,31,29,27,25,46,44,42,40,38,36,34,32,30,28,26)$
23B8 $23^{2}$ $44$ $23$ $44$ $( 1,12,23,11,22,10,21, 9,20, 8,19, 7,18, 6,17, 5,16, 4,15, 3,14, 2,13)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)$
23B9 $23^{2}$ $44$ $23$ $44$ $( 1,22,20,18,16,14,12,10, 8, 6, 4, 2,23,21,19,17,15,13,11, 9, 7, 5, 3)(24,28,32,36,40,44,25,29,33,37,41,45,26,30,34,38,42,46,27,31,35,39,43)$
23B10 $23^{2}$ $44$ $23$ $44$ $( 1, 9,17, 2,10,18, 3,11,19, 4,12,20, 5,13,21, 6,14,22, 7,15,23, 8,16)(24,31,38,45,29,36,43,27,34,41,25,32,39,46,30,37,44,28,35,42,26,33,40)$
23B11 $23^{2}$ $44$ $23$ $44$ $( 1,19,14, 9, 4,22,17,12, 7, 2,20,15,10, 5,23,18,13, 8, 3,21,16,11, 6)(24,34,44,31,41,28,38,25,35,45,32,42,29,39,26,36,46,33,43,30,40,27,37)$
46A $23,2^{11},1$ $1012$ $46$ $33$ $( 1,17)( 2,16)( 3,15)( 4,14)( 5,13)( 6,12)( 7,11)( 8,10)(18,23)(19,22)(20,21)(24,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25)$
46B1 $46$ $1012$ $46$ $45$ $( 1,46,11,26,21,29, 8,32,18,35, 5,38,15,41, 2,44,12,24,22,27, 9,30,19,33, 6,36,16,39, 3,42,13,45,23,25,10,28,20,31, 7,34,17,37, 4,40,14,43)$
46B3 $46$ $1012$ $46$ $45$ $( 1,26, 8,35,15,44,22,30, 6,39,13,25,20,34, 4,43,11,29,18,38, 2,24, 9,33,16,42,23,28, 7,37,14,46,21,32, 5,41,12,27,19,36, 3,45,10,31,17,40)$
46B5 $46$ $1012$ $46$ $45$ $( 1,29, 5,44, 9,36,13,28,17,43,21,35, 2,27, 6,42,10,34,14,26,18,41,22,33, 3,25, 7,40,11,32,15,24,19,39,23,31, 4,46, 8,38,12,30,16,45,20,37)$
46B7 $46$ $1012$ $46$ $45$ $( 1,32, 2,30, 3,28, 4,26, 5,24, 6,45, 7,43, 8,41, 9,39,10,37,11,35,12,33,13,31,14,29,15,27,16,25,17,46,18,44,19,42,20,40,21,38,22,36,23,34)$
46B9 $46$ $1012$ $46$ $45$ $( 1,35,22,39,20,43,18,24,16,28,14,32,12,36,10,40, 8,44, 6,25, 4,29, 2,33,23,37,21,41,19,45,17,26,15,30,13,34,11,38, 9,42, 7,46, 5,27, 3,31)$
46B11 $46$ $1012$ $46$ $45$ $( 1,38,19,25,14,35, 9,45, 4,32,22,42,17,29,12,39, 7,26, 2,36,20,46,15,33,10,43, 5,30,23,40,18,27,13,37, 8,24, 3,34,21,44,16,31,11,41, 6,28)$
46B13 $46$ $1012$ $46$ $45$ $( 1,41,16,34, 8,27,23,43,15,36, 7,29,22,45,14,38, 6,31,21,24,13,40, 5,33,20,26,12,42, 4,35,19,28,11,44, 3,37,18,30,10,46, 2,39,17,32, 9,25)$
46B15 $46$ $1012$ $46$ $45$ $( 1,44,13,43, 2,42,14,41, 3,40,15,39, 4,38,16,37, 5,36,17,35, 6,34,18,33, 7,32,19,31, 8,30,20,29, 9,28,21,27,10,26,22,25,11,24,23,46,12,45)$
46B17 $46$ $1012$ $46$ $45$ $( 1,24,10,29,19,34, 5,39,14,44,23,26, 9,31,18,36, 4,41,13,46,22,28, 8,33,17,38, 3,43,12,25,21,30, 7,35,16,40, 2,45,11,27,20,32, 6,37,15,42)$
46B19 $46$ $1012$ $46$ $45$ $( 1,27, 7,38,13,26,19,37, 2,25, 8,36,14,24,20,35, 3,46, 9,34,15,45,21,33, 4,44,10,32,16,43,22,31, 5,42,11,30,17,41,23,29, 6,40,12,28,18,39)$
46B21 $46$ $1012$ $46$ $45$ $( 1,30, 4,24, 7,41,10,35,13,29,16,46,19,40,22,34, 2,28, 5,45, 8,39,11,33,14,27,17,44,20,38,23,32, 3,26, 6,43, 9,37,12,31,15,25,18,42,21,36)$

Malle's constant $a(G)$:     $1/11$

Copy content comment:Conjugacy classes
 
Copy content magma:ConjugacyClasses(G);
 
Copy content sage:G.conjugacy_classes()
 
Copy content oscar:conjugacy_classes(G)
 
Copy content gap:ConjugacyClasses(G);
 

Character table

49 x 49 character table

Copy content comment:Character table
 
Copy content magma:CharacterTable(G);
 
Copy content sage:G.character_table()
 
Copy content oscar:character_table(G)
 
Copy content gap:CharacterTable(G);
 

Regular extensions

Data not computed