Properties

Label 19T8
Degree $19$
Order $1.216\times 10^{17}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $S_{19}$

Related objects

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Group action invariants

Degree $n$:  $19$
Transitive number $t$:  $8$
Group:  $S_{19}$
Parity:  $-1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19), (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

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

Conjugacy classes

There are 490 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $121645100408832000=2^{16} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.