Eccoci.

The Gauss Factorial of a number $n$ is defined as the product of all positive numbers $\le n$ that are relatively prime to $n$. For example $g(10)=1\times 3\times 7\times 9=189$.

Also we define $${\displaystyle G(n)=\prod _{i=1}^{n}g(i)}$$

You are given $G(10)=23044331520000$.

Find $G({10}^8)$. Give your answer modulo $1000000007$.