Properties

Label 19T7
Degree $19$
Order $6.082\times 10^{16}$
Cyclic no
Abelian no
Solvable no
Primitive yes
$p$-group no
Group: $A_{19}$

Related objects

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Group action invariants

Degree $n$:  $19$
Transitive number $t$:  $7$
Group:  $A_{19}$
Parity:  $1$
Primitive:  yes
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19), (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 254 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $60822550204416000=2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17 \cdot 19$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.