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Properties

Label 40T185333
Degree $40$
Order $50000000$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5^8.D_8.C_8$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 185333);
 

Group invariants

Abstract group:  $C_5^8.D_8.C_8$
Copy content magma:IdentifyGroup(G);
 
Order:  $50000000=2^{7} \cdot 5^{8}$
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 $t$:  $185333$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $1$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,22)(2,23,3,24,5,21,4,25)(6,28,7,29,9,26,8,30)(10,27)(11,32)(12,33,13,34,15,31,14,35)(16,39,19,40,20,37,17,36)(18,38)$, $(1,11,4,12,3,15,5,14)(2,13)(6,36,7,40,10,37,9,38)(8,39)(16,27)(17,26,18,30,20,28,19,29)(21,33)(22,32,23,31,25,34,24,35)$, $(1,9,13,39)(2,6,11,36,4,10,12,40,5,7,15,37,3,8,14,38)(16,24,29,32)(17,25,27,35,19,22,28,31,20,23,26,34,18,21,30,33)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_4$ x 4, $C_2^2$ x 7
$8$:  $D_{4}$ x 2, $C_8$ x 4, $C_4\times C_2$ x 6, $C_2^3$
$16$:  $D_4\times C_2$, $Q_8:C_2$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_4$ x 2, $C_2^2$

Degree 5: None

Degree 8: $C_4\times C_2$

Degree 10: None

Degree 20: None

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