Properties

Label 13T8
Degree $13$
Order $3113510400$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{13}$

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Group action invariants

Degree $n$:  $13$
Transitive number $t$:  $8$
Group:  $A_{13}$
CHM label:  $A13$
Parity:  $1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$\card{\Aut(F/K)}$:  $1$
Generators:  (3,4,5,6,7,8,9,10,11,12,13), (1,2,3)

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

There are 55 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $3113510400=2^{9} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
Cyclic:  no
Abelian:  no
Solvable:  no
Label:  not available
Character table: not available.