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Properties

Label 16T1841
16T1841 1 12 1->12 15 1->15 2 11 2->11 16 2->16 3 10 3->10 13 3->13 4 9 4->9 14 4->14 5 8 5->8 5->9 6 7 6->7 6->10 7->3 7->13 8->4 8->14 9->11 9->15 10->12 10->16 11->5 12->6 13->4 13->5 14->3 14->6 15->8 16->7
Degree $16$
Order $43008$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_2^7.F_8:C_6$

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Show commands: Magma

Copy content magma:G := TransitiveGroup(16, 1841);
 

Group invariants

Abstract group:  $C_2^7.F_8:C_6$
Copy content magma:IdentifyGroup(G);
 
Order:  $43008=2^{11} \cdot 3 \cdot 7$
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 $n$:  $16$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1841$
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:  $(1,15)(2,16)(3,10,12,6,7,13,4,9,11,5,8,14)$, $(1,12)(2,11)(3,13,5,9,15,8,4,14,6,10,16,7)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$21$:  $C_7:C_3$
$42$:  $(C_7:C_3) \times C_2$
$168$:  $C_2^3:(C_7: C_3)$
$336$:  14T18
$2688$:  16T1501
$21504$:  56T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 8: $C_2^3:(C_7: C_3)$

Low degree siblings

16T1841, 32T1515379

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

51 x 51 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed