The Noether number of the non-abelian group of order $$3p$$3p
It is proven that for any representation over a field of characteristic $$0$$0 of the non-abelian semidirect product of a cyclic group of prime order $$p$$p and the group of order $$3$$3 the corresponding algebra of polynomial invariants is generated by elements of degree at most $$p+2$$p+2. We also determine the exact universal degree bound for separating systems of polynomial invariants of this group in characteristic not dividing $$3p$$3p.