Properties

Label 13T9
Degree $13$
Order $6227020800$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{13}$

Related objects

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Group action invariants

Degree $n$:  $13$
Transitive number $t$:  $9$
Group:  $S_{13}$
CHM label:  $S13$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13), (1,2)

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

26T83

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 101 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $6227020800=2^{10} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.