Label 47T5
Degree $47$
Order $1.293\times 10^{59}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{47}$


Learn more

Show commands: Magma

magma: G := TransitiveGroup(47, 5);

Group action invariants

Degree $n$:  $47$
magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:  $5$
magma: t, n := TransitiveGroupIdentification(G); t;
Group:  $A_{47}$
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:  (1,2,3), (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)
magma: Generators(G);

Low degree resolvents


Resolvents shown for degrees $\leq 47$


Prime degree - 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

The 62494 conjugacy class representatives for $A_{47}$ are not computed

magma: ConjugacyClasses(G);

Group invariants

Order:  $129311620755584090321482177576805989984598816194560000000000=2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47$
magma: Order(G);
Cyclic:  no
magma: IsCyclic(G);
Abelian:  no
magma: IsAbelian(G);
Solvable:  no
magma: IsSolvable(G);
Nilpotency class:   not nilpotent
Label:  129311620755584090321482177576805989984598816194560000000000.a
magma: IdentifyGroup(G);
Character table:    not computed

magma: CharacterTable(G);