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Properties

Label 40T274346
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, 274346);
 

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 $t$:  $274346$
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:  $(1,28,4,29,5,26,2,30)(3,27)(6,21,10,24,7,23,8,25)(9,22)(11,17,14,18,13,16,15,20)(12,19)(31,38,34,39,35,36,32,40)(33,37)$, $(1,15)(2,14,4,12,5,11,3,13)(6,40,9,36,8,39,10,38)(7,37)(16,31)(17,34,19,35,20,33,18,32)(21,27,22,29,25,30,24,28)(23,26)$, $(1,6,4,7,2,8,5,9,3,10)(11,37,13,38,15,39,12,40,14,36)(16,31,20,34,18,35,19,32)(17,33)(21,28)(22,30,24,29,25,26,23,27)$, $(1,7,4,8,3,6,5,10)(2,9)(11,40)(12,36,13,37,15,39,14,38)(16,30,19,29,20,27,17,28)(18,26)(21,32,22,35,25,34,24,31)(23,33)$
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
$16$:  $D_4\times C_2$ x 42
$32$:  $C_2^2 \wr C_2$ x 28
$64$:  $(((C_4 \times C_2): C_2):C_2):C_2$ x 6

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