Properties

Label 41T9
Degree $41$
Order $1.673\times 10^{49}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{41}$

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Show commands: Magma

magma: G := TransitiveGroup(41, 9);
 

Group action invariants

Degree $n$:  $41$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $9$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $A_{41}$
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)
magma: Generators(G);
 

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

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 22365 conjugacy class representatives for $A_{41}$ are not computed

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $16726263306581903554085031026720375832576000000000=2^{37} \cdot 3^{18} \cdot 5^{9} \cdot 7^{5} \cdot 11^{3} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  no
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  16726263306581903554085031026720375832576000000000.a
magma: IdentifyGroup(G);
 
Character table:    not computed

magma: CharacterTable(G);