Consider the equation ${17}^{p}a+{19}^{p}b+{23}^{p}c=n$ where $a$, $b$, $c$ and $p$ are positive integers, i.e. $a,b,c,p>0$.

For a given $p$ there are some values of $n>0$ for which the equation cannot be solved. We call these unreachable values.

Define $G(p)$ to be the sum of all unreachable values of $n$ for the given value of $p$. For example $G(1)=8253$ and $G(2)=60258000$.

Find $G(6)$. Give your answer modulo $1000000007$.