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Properties

Label 16T1948
Degree $16$
Order $10321920$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no
Group: $C_2^8.S_8$

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Show commands: Magma

magma: G := TransitiveGroup(16, 1948);
 

Group action invariants

Degree $n$:  $16$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1948$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_2^8.S_8$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $2$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,8,11,3,6,14,15,10)(2,7,12,4,5,13,16,9), (1,13,12,16)(2,14,11,15)(7,9)(8,10), (1,2)(3,16,9,14,8,12)(4,15,10,13,7,11)
magma: Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$40320$:  $S_8$
$80640$:  16T1873
$5160960$:  56T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 8: $S_8$

Low degree siblings

16T1948 x 3, 32T2746190 x 2, 32T2746191 x 2, 32T2746192 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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $10321920=2^{15} \cdot 3^{2} \cdot 5 \cdot 7$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  10321920.a
magma: IdentifyGroup(G);
 
Character table:    not computed

magma: CharacterTable(G);