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.