Vampire fan club?

Logic Level 1

\[ \begin{array} {ccccc} \large & & \color{red}F & \color{blue}A & \color{green}N & \color{purple}G\\ \large + & & & \color{red}F& \color{blue}A & \color{green}N \\ \hline \large & & 3 & 1 & 2 & 2 \end{array} \]

Each letter represents a different nonzero digit. What is \(G?\)