In what kind of government dose a small group have a firm control over a country?

The form of government where a small group of people have a power control over a country is called oligarchy.

Explanation:

The people who consist the group can be considered as educated, wealthy, religious or more political. The type of countries with oligarchy are controlled by the families and are influenced from one generation to another.

This type of government often brings oppression to the public by not letting them to express themselves and their idea in the form in which they like. Another term that can used for this type of government is plutocracy, or as coined by Aristotle oligarchy can be termed as a country which is ruled by the elite class of people, or aristocrats.