Let $G$ be a finite group of order $2^7\cdot3^3\cdot5^2\cdot7$. Let $\mathrm{Irr}(G)$ be the set of all the irreducible $\mathbb{C}$-characters. Suppose that

(1) there is a character $\chi\in\mathrm{Irr}(G)$ such that $2^5\cdot7|\chi(1)$;

(2) there is a character $\theta\in\mathrm{Irr}(G)$ such that $5^2\cdot7|\theta(1)$;

(3) there is a character $\xi\in\mathrm{Irr}(G)$ such that $3^3\cdot7|\xi(1)$;

Question: Is $G$ non-solvable?