$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}$What is the abelianization of $\GL_n(\mathbb{Z})$? I know the abelianzation of $\GL_n(\mathbb{F})$ where $\mathbb{F}$ is a field and the abelianization of $ \SL_n(\mathbb{Z})$. However I can't find the abelianization of $\GL_n(\mathbb{Z})$ and I suspect this is something that should be well-known.