What is it called when one believes to be superior but objectively is not?

On a television documentary, a small group of people declared and truly believed themselves to be superior to other groups.

They referred to themselves as "thoroughbreds" citing physical, mental and behavioral superiority.

Objectively speaking, it's clear that it is false - that other groups can outperform them in all those aspects. (or at least for this question, lets say they would not end up scoring first place on objective tests for those attributes).

What is this phenomenon called ?

(Please note, this question has nothing to do with any single group. This concept is actually seen across many different groups, which in itself, is a complete paradox).

Solution 1:

Delusional. Otherwise, a term like superiority complex seems most appropriate.