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Properties

Label 40T106038
Degree $40$
Order $204800$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9.C_5^2:\OD_{16}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 106038);
 

Group invariants

Abstract group:  $C_2^9.C_5^2:\OD_{16}$
Copy content magma:IdentifyGroup(G);
 
Order:  $204800=2^{13} \cdot 5^{2}$
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 $t$:  $106038$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $4$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,15,12,38,27,8,18,23)(2,16,11,37,28,7,17,24)(3,13,9,40,25,5,19,21)(4,14,10,39,26,6,20,22)(29,36,32,33)(30,35,31,34)$, $(1,4)(2,3)(5,29,24,40)(6,30,23,39)(7,32,21,37)(8,31,22,38)(9,18,33,25,10,17,34,26)(11,20,36,28,12,19,35,27)(13,15)(14,16)$, $(1,22,26,13,34,39,12,5)(2,21,25,14,33,40,11,6)(3,24,28,15,36,37,9,8)(4,23,27,16,35,38,10,7)(17,31,19,30)(18,32,20,29)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_4$ x 4, $C_2^2$ x 7
$8$:  $C_4\times C_2$ x 6, $C_2^3$
$16$:  $C_8:C_2$ x 2, $C_4\times C_2^2$
$32$:  $C_2 \times (C_8:C_2)$
$400$:  $(C_5^2 : C_8):C_2$
$800$:  20T162
$102400$:  20T770

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 5: None

Degree 8: None

Degree 10: $(C_5^2 : C_8):C_2$

Degree 20: 20T109, 20T865, 20T866

Low degree siblings

20T865 x 2, 20T866 x 2, 40T106016 x 2, 40T106033 x 2, 40T106035 x 2, 40T106037 x 2, 40T106038, 40T106081, 40T106082, 40T106120 x 2, 40T106121 x 2, 40T106122 x 2, 40T106123 x 2, 40T106128 x 2, 40T106129 x 2, 40T106130 x 2, 40T106131 x 2, 40T106226 x 2, 40T106228 x 2

Siblings are shown with degree $\leq 47$

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

98 x 98 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed