Moderate# Quotient by the Center: What Does It Hide?

ABSALG-JR@MOY

Recall that for every group $G$, the center $Z(G)$ of $G$ is the set of elements in $G$ that commute with every element in $G$, that is:

$$Z(G)=\{x\in G:xg=gx\; \; \text{for all}\; \; g\in G\}$$

It is clear that $Z(G)$ is a normal subgroup of $G$.

Which of the following facts is true about the quotient group $G/Z(G)$?