Properties

Label 28T1854
Degree $28$
Order $3.049\times 10^{29}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{28}$

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Show commands: Magma

magma: G := TransitiveGroup(28, 1854);
 

Group action invariants

Degree $n$:  $28$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1854$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $S_{28}$
Parity:  $-1$
magma: IsEven(G);
 
Primitive:  yes
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,2), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 7: None

Degree 14: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 3,718 conjugacy classes of elements. Data not shown.

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $304888344611713860501504000000=2^{25} \cdot 3^{13} \cdot 5^{6} \cdot 7^{4} \cdot 11^{2} \cdot 13^{2} \cdot 17 \cdot 19 \cdot 23$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  304888344611713860501504000000.a
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);