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Properties

Label 40T274231
Degree $40$
Order $6400000000$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_5^7.(C_2^3\times F_5).D_4^2:D_4$

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Copy content magma:G := TransitiveGroup(40, 274231);
 

Group invariants

Abstract group:  $C_5^7.(C_2^3\times F_5).D_4^2:D_4$
Copy content magma:IdentifyGroup(G);
 
Order:  $6400000000=2^{14} \cdot 5^{8}$
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 $t$:  $274231$
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:  $(1,28,5,30,3,29,4,27)(2,26)(6,21)(7,25,8,24,10,22,9,23)(11,18,14,19,15,16,12,20)(13,17)(31,37,34,39,35,38,32,36)(33,40)$, $(1,24,37,16,2,23,39,17,4,21,38,19,3,22,36,18)(5,25,40,20)(6,27,12,31)(7,26,11,32,9,29,14,34,10,28,13,35,8,30,15,33)$, $(1,3,2,5)(6,8,10,7,9)(11,15,13,14)(16,25,19,21,18,24,20,23)(17,22)(26,33,28,34,27,31,30,35)(29,32)(37,40)(38,39)$, $(1,19,36,24)(2,20,40,25,4,17,38,22,5,18,37,23,3,16,39,21)(6,34,13,27)(7,35,12,29,8,31,11,26,10,33,14,30,9,32,15,28)$
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 28, $C_2^3$ x 15
$16$:  $QD_{16}$ x 4, $D_4\times C_2$ x 42
$32$:  $Z_8 : Z_8^\times$ x 6, $C_2^2 \wr C_2$ x 28
$64$:  $(((C_4 \times C_2): C_2):C_2):C_2$ x 6
$128$:  $C_2 \wr C_2\wr C_2$ x 8

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$, $D_{4}$ x 2

Degree 5: None

Degree 8: $D_4\times C_2$

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