# Group theory Finite group that has no decomposition of a given cardinality.

I'm looking for an example of a finite group. $$G$$ whose order can be written as a product $$| G | = ab$$ of two numbers $$a, b$$ such that $$AB ne G$$ for any subset $$A, B G subset$$ of cardinality $$| A | = a$$ Y $$| B | = b$$.

**Observation. ** Such a group $$G$$ it can not be abelian and also $$G$$ they do not contain cardinality subgroups $$a$$ or $$b$$.