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Properties

Label 46T37
46T37 1 10 1->10 17 1->17 2 9 2->9 18 2->18 3 7 3->7 24 3->24 4 8 4->8 23 4->23 5 6 5->6 29 5->29 30 6->30 7->4 35 7->35 8->3 36 8->36 9->1 41 9->41 10->2 42 10->42 11 11->2 46 11->46 12 12->1 45 12->45 13 13->7 43 13->43 14 14->8 44 14->44 15 15->14 15->41 16 16->13 16->42 19 17->19 40 17->40 20 18->20 39 18->39 25 19->25 37 19->37 26 20->26 38 20->38 21 31 21->31 21->36 22 32 22->32 22->35 34 23->34 23->38 33 24->33 24->37 25->32 25->43 26->31 26->44 27 27->3 27->29 28 28->4 28->30 29->9 29->28 30->10 30->27 31->16 31->25 32->15 32->26 33->21 33->23 34->22 34->24 35->21 35->27 36->22 36->28 37->33 38->34 41->46 42->45 43->6 44->5 45->11 46->12
Degree $46$
Order $4244635648$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^{22}.C_{46}.C_{22}$

Related objects

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Show commands: Magma

Copy content magma:G := TransitiveGroup(46, 37);
 

Group invariants

Abstract group:  $C_2^{22}.C_{46}.C_{22}$
Copy content magma:IdentifyGroup(G);
 
Order:  $4244635648=2^{24} \cdot 11 \cdot 23$
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 $t$:  $37$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $-1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,17,19,25,43,6,30,10,42,45,11,2,18,20,26,44,5,29,9,41,46,12)(3,24,37,33,21,31,16,13,7,35,27)(4,23,38,34,22,32,15,14,8,36,28)$, $(1,10,2,9)(3,7,4,8)(5,6)(11,46)(12,45)(13,43)(14,44)(15,41)(16,42)(17,40)(18,39)(19,37)(20,38)(21,36,22,35)(23,34,24,33)(25,32,26,31)(27,29,28,30)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$11$:  $C_{11}$
$22$:  22T1 x 3
$44$:  44T2
$506$:  $F_{23}$
$1012$:  46T6
$2122317824$:  46T35

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $F_{23}$

Low degree siblings

46T37

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Conjugacy classes not computed

Copy content magma:ConjugacyClasses(G);
 

Character table

Character table not computed

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed