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Properties

Label 40T1013
Degree $40$
Order $1280$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^6:D_{10}$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 1013);
 

Group invariants

Abstract group:  $C_2^6:D_{10}$
Copy content magma:IdentifyGroup(G);
 
Order:  $1280=2^{8} \cdot 5$
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 $t$:  $1013$
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:  $(1,37,4,40)(2,38,3,39)(5,33,7,36)(6,34,8,35)(9,31,11,30)(10,32,12,29)(13,27,16,25)(14,28,15,26)(17,23,20,22)(18,24,19,21)$, $(1,22)(2,21)(3,24)(4,23)(5,26)(6,25)(7,28)(8,27)(9,32)(10,31)(11,29)(12,30)(13,36)(14,35)(15,34)(16,33)(17,40)(18,39)(19,38)(20,37)$, $(1,13,4,16)(2,14,3,15)(5,10,7,12)(6,9,8,11)(17,40,20,37)(18,39,19,38)(21,34,24,35)(22,33,23,36)(25,30,27,31)(26,29,28,32)$
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
$8$:  $D_{4}$ x 2, $C_2^3$
$10$:  $D_{5}$
$16$:  $D_4\times C_2$
$20$:  $D_{10}$ x 3
$40$:  20T7 x 2, 20T8
$80$:  40T24
$160$:  $(C_2^4 : C_5) : C_2$
$320$:  $C_2\times (C_2^4 : D_5)$ x 3
$640$:  20T136 x 2, 20T141

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 5: $D_{5}$

Degree 8: None

Degree 10: $D_{10}$, $C_2\times (C_2^4 : D_5)$ x 2

Degree 20: 20T7, 20T141, 20T142

Low degree siblings

40T1002 x 6, 40T1013 x 11, 40T1019 x 6, 40T1040 x 12, 40T1131 x 12, 40T1132 x 24, 40T1133 x 48, 40T1158 x 48, 40T1159 x 48, 40T1169 x 12

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

56 x 56 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed