What is a social group?

a social group is a number of individuals interacting with each other with respect to:

1. Common motives and goals;
2. An accepted division of labor, i.e. roles,
3. Established status (social rank, dominance) relationships;
4. Accepted norms and values with reference to matters relevant to the group;
5. Development of accepted sanctions (praise and punishment) if and when norms

or short and simple:

A group of people who interact with each other and are aware of having something in common.