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Properties

Label 40T314390
Degree $40$
Order $4.300\times 10^{16}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $A_5^8.C_2\wr C_4.C_2^2$

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Copy content magma:G := TransitiveGroup(40, 314390);
 

Group invariants

Abstract group:  $A_5^8.C_2\wr C_4.C_2^2$
Copy content magma:IdentifyGroup(G);
 
Order:  $42998169600000000=2^{24} \cdot 3^{8} \cdot 5^{8}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  no
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 $t$:  $314390$
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:  $(1,4)(6,9,10,7,8)(12,13)(14,15)(16,22,18,24,17,25,19,23,20,21)(26,33)(27,32,30,34,29,31)(28,35)(36,40,38,39)$, $(1,5)(3,4)(6,10,7,8,9)(11,14)(12,13)(16,26,18,30,19,27,20,29)(17,28)(21,32,25,33)(22,35)(23,31)(24,34)(36,40,38)$, $(1,3,2)(4,5)(6,10,8,9,7)(11,15,12)(13,14)(17,20,19,18)(21,22,25,23,24)(26,30,28,27)(31,35,33,32,34)(36,39,38,37,40)$, $(1,18,5,16,4,20,3,19)(2,17)(6,35,7,34,10,32,9,31)(8,33)(11,27,12,29,14,28,13,30)(15,26)(21,40,25,37,24,39,22,36)(23,38)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 15
$4$:  $C_2^2$ x 35
$8$:  $D_{4}$ x 12, $C_2^3$ x 15
$16$:  $D_4\times C_2$ x 18
$32$:  $C_2^2 \wr C_2$ x 4
$64$:  $(((C_4 \times C_2): C_2):C_2):C_2$ x 2

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$ x 3

Degree 5: None

Degree 8: $C_2^2 \wr C_2$

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