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Properties

Label 40T385
Degree $40$
Order $400$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $D_{10}.D_{10}$

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Copy content magma:G := TransitiveGroup(40, 385);
 

Group invariants

Abstract group:  $D_{10}.D_{10}$
Copy content magma:IdentifyGroup(G);
 
Order:  $400=2^{4} \cdot 5^{2}$
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 $t$:  $385$
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:  $(1,36,2,35)(3,33,4,34)(5,7,6,8)(9,27,10,28)(11,25,12,26)(13,37,14,38)(15,39,16,40)(17,20,18,19)(21,29,22,30)(23,31,24,32)$, $(1,40,2,39)(3,38,4,37)(5,34,6,33)(7,36,8,35)(9,31,10,32)(11,30,12,29)(13,27,14,28)(15,26,16,25)(17,22,18,21)(19,24,20,23)$, $(1,8,28,22,12,37,34,15,20,32,2,7,27,21,11,38,33,16,19,31)(3,6,26,23,9,39,36,14,17,30,4,5,25,24,10,40,35,13,18,29)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$8$:  $C_2^3$
$10$:  $D_{5}$ x 2
$16$:  $Q_8:C_2$
$20$:  $D_{10}$ x 6
$40$:  20T8 x 2
$80$:  40T21, 40T23
$100$:  $D_5^2$
$200$:  20T59

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 5: None

Degree 8: $Q_8:C_2$

Degree 10: $D_5^2$

Degree 20: 20T59

Low degree siblings

40T315 x 2, 40T385

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

52 x 52 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed