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Properties

Label 40T17357
Degree $40$
Order $40960$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^5.C_2^8:C_5$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 17357);
 

Group invariants

Abstract group:  $C_2^5.C_2^8:C_5$
Copy content magma:IdentifyGroup(G);
 
Order:  $40960=2^{13} \cdot 5$
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 $t$:  $17357$
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:  $(3,4)(5,6)(9,10)(11,12)(19,20)(21,22)(25,28,26,27)(29,31,30,32)(33,35,34,36)(37,39,38,40)$, $(1,30,35,22,12)(2,29,36,21,11)(3,32,34,23,9)(4,31,33,24,10)(5,27,38,18,13)(6,28,37,17,14)(7,25,39,19,16)(8,26,40,20,15)$, $(1,10,17,37,30,2,9,18,38,29)(3,11,19,39,31,4,12,20,40,32)(5,16,22,35,28,6,15,21,36,27)(7,13,24,33,25,8,14,23,34,26)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$5$:  $C_5$
$80$:  $C_2^4 : C_5$ x 17
$1280$:  20T190
$2560$:  32T205515

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $C_5$

Degree 8: None

Degree 10: $C_2^4 : C_5$ x 3

Degree 20: 20T190

Low degree siblings

40T17177 x 16, 40T17193 x 16, 40T17357 x 15, 40T17534 x 16, 40T17538 x 16, 40T17843 x 16

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