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Properties

Label 40T12858
Degree $40$
Order $20480$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^9.(C_2\times F_5)$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 12858);
 

Group invariants

Abstract group:  $C_2^9.(C_2\times F_5)$
Copy content magma:IdentifyGroup(G);
 
Order:  $20480=2^{12} \cdot 5$
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 $t$:  $12858$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $2$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,26,10,15,39,2,25,9,16,40)(3,28,11,14,37,4,27,12,13,38)(5,31,33,20,22)(6,32,34,19,21)(7,29,35,17,24)(8,30,36,18,23)$, $(1,13,17,26,23,35,39,5)(2,14,18,25,24,36,40,6)(3,15,20,27,21,34,37,8)(4,16,19,28,22,33,38,7)(9,11,10,12)(31,32)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $D_{4}$ x 2, $C_4\times C_2$
$16$:  $C_2^2:C_4$
$20$:  $F_5$
$40$:  $F_{5}\times C_2$
$80$:  20T19
$320$:  $(C_2^4 : C_5):C_4$
$640$:  $((C_2^4 : C_5):C_4)\times C_2$
$1280$:  20T191
$10240$:  20T416

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $F_5$

Degree 8: None

Degree 10: $(C_2^4 : C_5):C_4$

Degree 20: 20T77

Low degree siblings

20T514 x 4, 20T530 x 4, 40T11336 x 4, 40T11339 x 2, 40T11360 x 2, 40T11364 x 2, 40T11373 x 2, 40T11378 x 2, 40T11390 x 4, 40T11391 x 4, 40T12858, 40T12860 x 4, 40T12876 x 2, 40T12878 x 2, 40T12880 x 2, 40T12988 x 2, 40T12991 x 2, 40T12992 x 4, 40T13368 x 2, 40T13429 x 2, 40T13440 x 4, 40T13454 x 4, 40T13593 x 2, 40T13608 x 2, 40T14049 x 4, 40T14050 x 4, 40T14163 x 2, 40T14167 x 2, 40T14170 x 2, 40T14175 x 2

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

74 x 74 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed