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Properties

Label 46T2
46T2 1 4 1->4 11 1->11 2 3 2->3 12 2->12 13 3->13 14 4->14 5 15 5->15 46 5->46 6 16 6->16 45 6->45 7 18 7->18 43 7->43 8 17 8->17 44 8->44 9 19 9->19 41 9->41 10 20 10->20 42 10->42 21 11->21 40 11->40 22 12->22 39 12->39 23 13->23 37 13->37 24 14->24 38 14->38 25 15->25 35 15->35 26 16->26 36 16->36 28 17->28 34 17->34 27 18->27 33 18->33 29 19->29 31 19->31 30 20->30 32 20->32 21->29 21->31 22->30 22->32 23->28 23->34 24->27 24->33 25->26 25->36 26->35 27->38 28->37 29->40 30->39 31->41 32->42 33->43 34->44 35->46 36->45 37->2 38->1 39->3 40->4 41->6 42->5 43->8 44->7 45->9 46->10
Degree $46$
Order $46$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{23}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 2);
 

Group invariants

Abstract group:  $D_{23}$
Copy content magma:IdentifyGroup(G);
 
Order:  $46=2 \cdot 23$
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 $n$:  $46$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $2$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $46$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,4)(2,3)(5,46)(6,45)(7,43)(8,44)(9,41)(10,42)(11,40)(12,39)(13,37)(14,38)(15,35)(16,36)(17,34)(18,33)(19,31)(20,32)(21,29)(22,30)(23,28)(24,27)(25,26)$, $(1,11,21,31,41,6,16,26,35,46,10,20,30,39,3,13,23,34,44,7,18,27,38)(2,12,22,32,42,5,15,25,36,45,9,19,29,40,4,14,24,33,43,8,17,28,37)$
Copy content magma:Generators(G);
 

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $D_{23}$

Low degree siblings

23T2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{46}$ $1$ $1$ $0$ $()$
2A $2^{23}$ $23$ $2$ $23$ $( 1,22)( 2,21)( 3,19)( 4,20)( 5,18)( 6,17)( 7,15)( 8,16)( 9,13)(10,14)(11,12)(23,45)(24,46)(25,44)(26,43)(27,42)(28,41)(29,39)(30,40)(31,37)(32,38)(33,35)(34,36)$
23A1 $23^{2}$ $2$ $23$ $44$ $( 1, 7,13,20,26,31,38,44, 3,10,16,21,27,34,39,46, 6,11,18,23,30,35,41)( 2, 8,14,19,25,32,37,43, 4, 9,15,22,28,33,40,45, 5,12,17,24,29,36,42)$
23A2 $23^{2}$ $2$ $23$ $44$ $( 1,13,26,38, 3,16,27,39, 6,18,30,41, 7,20,31,44,10,21,34,46,11,23,35)( 2,14,25,37, 4,15,28,40, 5,17,29,42, 8,19,32,43, 9,22,33,45,12,24,36)$
23A3 $23^{2}$ $2$ $23$ $44$ $( 1,20,38,10,27,46,18,35, 7,26,44,16,34, 6,23,41,13,31, 3,21,39,11,30)( 2,19,37, 9,28,45,17,36, 8,25,43,15,33, 5,24,42,14,32, 4,22,40,12,29)$
23A4 $23^{2}$ $2$ $23$ $44$ $( 1,26, 3,27, 6,30, 7,31,10,34,11,35,13,38,16,39,18,41,20,44,21,46,23)( 2,25, 4,28, 5,29, 8,32, 9,33,12,36,14,37,15,40,17,42,19,43,22,45,24)$
23A5 $23^{2}$ $2$ $23$ $44$ $( 1,31,16,46,30,13,44,27,11,41,26,10,39,23, 7,38,21, 6,35,20, 3,34,18)( 2,32,15,45,29,14,43,28,12,42,25, 9,40,24, 8,37,22, 5,36,19, 4,33,17)$
23A6 $23^{2}$ $2$ $23$ $44$ $( 1,38,27,18, 7,44,34,23,13, 3,39,30,20,10,46,35,26,16, 6,41,31,21,11)( 2,37,28,17, 8,43,33,24,14, 4,40,29,19, 9,45,36,25,15, 5,42,32,22,12)$
23A7 $23^{2}$ $2$ $23$ $44$ $( 1,44,39,35,31,27,23,20,16,11, 7, 3,46,41,38,34,30,26,21,18,13,10, 6)( 2,43,40,36,32,28,24,19,15,12, 8, 4,45,42,37,33,29,25,22,17,14, 9, 5)$
23A8 $23^{2}$ $2$ $23$ $44$ $( 1, 3, 6, 7,10,11,13,16,18,20,21,23,26,27,30,31,34,35,38,39,41,44,46)( 2, 4, 5, 8, 9,12,14,15,17,19,22,24,25,28,29,32,33,36,37,40,42,43,45)$
23A9 $23^{2}$ $2$ $23$ $44$ $( 1,10,18,26,34,41, 3,11,20,27,35,44, 6,13,21,30,38,46, 7,16,23,31,39)( 2, 9,17,25,33,42, 4,12,19,28,36,43, 5,14,22,29,37,45, 8,15,24,32,40)$
23A10 $23^{2}$ $2$ $23$ $44$ $( 1,16,30,44,11,26,39, 7,21,35, 3,18,31,46,13,27,41,10,23,38, 6,20,34)( 2,15,29,43,12,25,40, 8,22,36, 4,17,32,45,14,28,42, 9,24,37, 5,19,33)$
23A11 $23^{2}$ $2$ $23$ $44$ $( 1,21,41,16,35,10,30, 3,23,44,18,38,11,31, 6,26,46,20,39,13,34, 7,27)( 2,22,42,15,36, 9,29, 4,24,43,17,37,12,32, 5,25,45,19,40,14,33, 8,28)$

Malle's constant $a(G)$:     $1/23$

Copy content magma:ConjugacyClasses(G);
 

Character table

1A 2A 23A1 23A2 23A3 23A4 23A5 23A6 23A7 23A8 23A9 23A10 23A11
Size 1 23 2 2 2 2 2 2 2 2 2 2 2
2 P 1A 1A 23A2 23A4 23A6 23A8 23A10 23A11 23A9 23A7 23A5 23A3 23A1
23 P 1A 2A 23A11 23A1 23A10 23A2 23A9 23A3 23A8 23A4 23A7 23A5 23A6
Type
46.1.1a R 1 1 1 1 1 1 1 1 1 1 1 1 1
46.1.1b R 1 −1 1 1 1 1 1 1 1 1 1 1 1
46.1.2a1 R 2 0 ζ23−11+ζ2311 ζ23−7+ζ237 ζ23−3+ζ233 ζ23−1+ζ23 ζ23−5+ζ235 ζ23−9+ζ239 ζ23−10+ζ2310 ζ23−6+ζ236 ζ23−2+ζ232 ζ23−4+ζ234 ζ23−8+ζ238
46.1.2a2 R 2 0 ζ23−10+ζ2310 ζ23−2+ζ232 ζ23−9+ζ239 ζ23−3+ζ233 ζ23−8+ζ238 ζ23−4+ζ234 ζ23−7+ζ237 ζ23−5+ζ235 ζ23−6+ζ236 ζ23−11+ζ2311 ζ23−1+ζ23
46.1.2a3 R 2 0 ζ23−9+ζ239 ζ23−11+ζ2311 ζ23−8+ζ238 ζ23−5+ζ235 ζ23−2+ζ232 ζ23−1+ζ23 ζ23−4+ζ234 ζ23−7+ζ237 ζ23−10+ζ2310 ζ23−3+ζ233 ζ23−6+ζ236
46.1.2a4 R 2 0 ζ23−8+ζ238 ζ23−3+ζ233 ζ23−2+ζ232 ζ23−7+ζ237 ζ23−11+ζ2311 ζ23−6+ζ236 ζ23−1+ζ23 ζ23−4+ζ234 ζ23−9+ζ239 ζ23−5+ζ235 ζ23−10+ζ2310
46.1.2a5 R 2 0 ζ23−7+ζ237 ζ23−6+ζ236 ζ23−4+ζ234 ζ23−9+ζ239 ζ23−1+ζ23 ζ23−11+ζ2311 ζ23−2+ζ232 ζ23−8+ζ238 ζ23−5+ζ235 ζ23−10+ζ2310 ζ23−3+ζ233
46.1.2a6 R 2 0 ζ23−6+ζ236 ζ23−8+ζ238 ζ23−10+ζ2310 ζ23−11+ζ2311 ζ23−9+ζ239 ζ23−7+ζ237 ζ23−5+ζ235 ζ23−3+ζ233 ζ23−1+ζ23 ζ23−2+ζ232 ζ23−4+ζ234
46.1.2a7 R 2 0 ζ23−5+ζ235 ζ23−1+ζ23 ζ23−7+ζ237 ζ23−10+ζ2310 ζ23−4+ζ234 ζ23−2+ζ232 ζ23−8+ζ238 ζ23−9+ζ239 ζ23−3+ζ233 ζ23−6+ζ236 ζ23−11+ζ2311
46.1.2a8 R 2 0 ζ23−4+ζ234 ζ23−10+ζ2310 ζ23−1+ζ23 ζ23−8+ζ238 ζ23−6+ζ236 ζ23−3+ζ233 ζ23−11+ζ2311 ζ23−2+ζ232 ζ23−7+ζ237 ζ23−9+ζ239 ζ23−5+ζ235
46.1.2a9 R 2 0 ζ23−3+ζ233 ζ23−4+ζ234 ζ23−5+ζ235 ζ23−6+ζ236 ζ23−7+ζ237 ζ23−8+ζ238 ζ23−9+ζ239 ζ23−10+ζ2310 ζ23−11+ζ2311 ζ23−1+ζ23 ζ23−2+ζ232
46.1.2a10 R 2 0 ζ23−2+ζ232 ζ23−5+ζ235 ζ23−11+ζ2311 ζ23−4+ζ234 ζ23−3+ζ233 ζ23−10+ζ2310 ζ23−6+ζ236 ζ23−1+ζ23 ζ23−8+ζ238 ζ23−7+ζ237 ζ23−9+ζ239
46.1.2a11 R 2 0 ζ23−1+ζ23 ζ23−9+ζ239 ζ23−6+ζ236 ζ23−2+ζ232 ζ23−10+ζ2310 ζ23−5+ζ235 ζ23−3+ζ233 ζ23−11+ζ2311 ζ23−4+ζ234 ζ23−8+ζ238 ζ23−7+ζ237

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed