# Complexity class of an algorithm

What is the complexity class of an algorithm that runs in $$n^{\mathcal{O}(\sqrt{n}log(n))}$$ time?

As $$n$$ gets large $$\sqrt{n}log(n)$$ increases at a very slow rate. Does this mean that the algorithm has the same complexity as $$n^{\mathcal{O}(1)}$$, which would be in $$P$$?

No, $$\sqrt{n}$$ increases far faster than $$O(1)$$, and $$n^{\sqrt{n}}$$ grows far faster than $$n^{O(1)}$$. No, it certainly does not have the same runtime. See Sorting functions by asymptotic growth.
There may be no predefined complexity class; the complexity class is the class of all algorithms who run in time $$n^{O(\sqrt{n} \log n)}$$, and there's probably not much more to say.
• Thank you for your response. Just to be clear, your saying it's inconclusive whether this is in $P$ or Sharp-$P$, right? – Teferi Mar 27 at 13:33