Is there any standard terminology for the quotient of a topological group by the connected component of the identity?

Question

If $G$ is any topological group, then the connected component of its identity is a closed normal subgroup $H$. It follows that $G/H$ is a totally disconnected topological group. Often, $G$ will be locally-connected in which case $G/H$ will even be discrete.

The group $G/H$ seems rather important, its elements are the components of $G$. Yet, I am not aware of any standard terminology or notation for $G/H$. Does anyone know of any?

Answer 1

I think it is called the component group of $G$, as the group $\pi_0(G)$ of connected components of $G$ is naturally isomorphic to $G/H$.