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Properties

Label 20T333
20T333 1 5 1->5 2 6 2->6 3 4 3->4 7 3->7 8 4->8 5->7 16 5->16 6->8 15 6->15 7->6 13 7->13 8->5 14 8->14 9 18 9->18 10 17 10->17 11 12 11->12 19 11->19 20 12->20 13->11 13->14 14->12 15->10 16->9 17->2 17->18 18->1 19->3 20->4
Degree $20$
Order $5120$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^8.C_{20}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(20, 333);
 

Group invariants

Abstract group:  $C_2^8.C_{20}$
Copy content magma:IdentifyGroup(G);
 
Order:  $5120=2^{10} \cdot 5$
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 $n$:  $20$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $333$
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:  $(1,5,16,9,18)(2,6,15,10,17)(3,7,13,11,19)(4,8,14,12,20)$, $(3,4)(5,7,6,8)(11,12)(13,14)(17,18)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$5$:  $C_5$
$10$:  $C_{10}$
$20$:  20T1
$80$:  $C_2^4 : C_5$
$160$:  $C_2 \times (C_2^4 : C_5)$
$320$:  20T75
$2560$:  20T256

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $C_5$

Degree 10: $C_2 \times (C_2^4 : C_5)$

Low degree siblings

20T333 x 23, 20T344 x 24, 40T3051 x 24, 40T3956 x 48, 40T4002 x 48, 40T4321 x 48, 40T4511 x 24, 40T4518 x 48, 40T4520 x 48, 40T4526 x 48, 40T4533 x 24, 40T4695 x 24, 40T4812 x 24, 40T4813 x 48, 40T4814 x 96, 40T4815 x 96, 40T4816 x 96, 40T5057 x 24, 40T5060 x 24, 40T5061 x 48, 40T5064 x 48, 40T5066 x 48, 40T5067 x 48, 40T5070 x 48, 40T5071 x 96, 40T5074 x 96, 40T5075 x 96, 40T5078 x 96, 40T5079 x 96, 40T5082 x 96, 40T5083 x 96, 40T5085 x 96, 40T5088 x 96, 40T5090 x 96, 40T5091 x 96, 40T5093 x 96, 40T5096 x 96, 40T5097 x 96, 40T5100 x 96, 40T5101 x 96, 40T5104 x 96, 40T5105 x 96, 40T5108 x 96, 40T5109 x 96, 40T5112 x 96, 40T5113 x 96, 40T5115 x 96, 40T5118 x 96, 40T5120 x 96

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

80 x 80 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed