A system's total momentum is conserved if it has no net external forces

up:: Linear Momentum Conservation Theorem

When the sum of external forces is equal to $0$, we have that the system’s total momentum

$$\vec{P}=\sum _{i=1}^n{m}_i{v}_i=\sum _{i=1}^n{m}_i\frac{d{\vec{r}}_i}{dt}=M\frac{d\vec{R}}{dt}$$

is conserved.

In this case, the Center of Mass is moving uniformly ─ regardless whether its constituent particles aren’t!