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Properties

Label 40T100976
Degree $40$
Order $163840$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9.C_2^5:C_{10}$

Related objects

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 100976);
 

Group invariants

Abstract group:  $C_2^9.C_2^5:C_{10}$
Copy content magma:IdentifyGroup(G);
 
Order:  $163840=2^{15} \cdot 5$
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 $n$:  $40$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $100976$
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:  $(1,40,17,30,13,5,34,22,28,10,2,39,18,29,14,6,33,21,27,9)(3,37,20,32,15,8,35,23,26,11,4,38,19,31,16,7,36,24,25,12)$, $(1,33,17,27,12,4,36,20,26,10,2,34,18,28,11,3,35,19,25,9)(5,39,21,29,16,8,37,23,31,14,6,40,22,30,15,7,38,24,32,13)$, $(1,25,33,11,21,5,31,40,15,18,2,26,34,12,22,6,32,39,16,17)(3,28,35,9,24,8,30,38,14,19,4,27,36,10,23,7,29,37,13,20)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5$:  $C_5$
$10$:  $C_{10}$ x 3
$80$:  $C_2^4 : C_5$ x 17
$160$:  $C_2 \times (C_2^4 : C_5)$ x 51

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $C_5$

Degree 8: None

Degree 10: $C_2 \times (C_2^4 : C_5)$ x 3

Degree 20: 20T341

Low degree siblings

There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

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