# Properties

 Label 19T7 Order $$60822550204416000$$ n $$19$$ Cyclic No Abelian No Solvable No Primitive Yes $p$-group No Group: $A_{19}$

# Learn more about

## Group action invariants

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

## 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: Data not available
 Character table: Data not available.