Stem group has the minimum order among all groups isoclinic to it

Statement
Suppose $$G$$ is a stem group (i.e., $$Z(G) \le [G,G]$$) and $$H$$ is a group that is  isoclinic to $$G$$. Then, the order of $$G$$ is less than or equal to the order of $$H$$. This statement holds both in the case of finite groups (where the order is just a finite number) and infinite groups (if we use infinite cardinals).

In the finite case, it is further true that the order of $$G$$ divides the order of $$H$$.

Related facts

 * Every group is isoclinic to a stem group

Journal references

 * : Page 135 (Page 6 within the paper) alludes to this fact in the finite context, with a proof of sorts around the statement.