# Definition(s) > [!NOTE] Definition (Direct Product of Groups) > Let $(G,\circ_{1})$ and $(H,\circ_{2})$ be [[Groups|groups]]. Let $G\times H$ be their [[Cartesian Product|cartesian product]]. The **(external) direct product** of $(G,\circ_{1})$ and $(H,\circ_{2})$ is the group $(G\times H,\circ)$ where the operation $\circ$ is defined as: $(g_{1},h_{1})\circ (g_{2},h_{2})= (g_{1}\circ_{1}g_{2},h_{1}\circ_{2}h_{2})$where $G\times H$ is the [[Cartesian Product|cartesian product]] of $G$ and $H$ (i.e. the set of ordered pairs $(g,h)$ where $g\in G$ and $h\in H.$) > [!Example] > Contents # Properties We get [[Direct Product of Groups is Group]].