Introduction to Quadras

Quadras are a method of grouping in socionics, where each quadra consists of a group of types that value the same functions. Types of the same quadra share similar values, interests, and communication preferences due to their valued functions.

Socionics types are divided into 4 quadras: Alpha, Beta, Gamma, and Delta.

Alpha Quadra values Ti, Fe, Si, and Ne. 
Beta Quadra values Ti, Fe, Se, and Ni. 
Gamma Quadra values Te, Fi, Se, and Ni. 
Delta Quadra values Te, Fi, Si, and Ne. 

Function strength in the types doesn’t affect quadral values, because these discuss preference in atmosphere and life rather than main actions and thought processes (the latter depending instead on individual type).

Here is an example on how valued functions manifest as quadral values, taken from wikisocion:

“Types that value extroverted thinking tend to focus on worthwhile or beneficial activity (what is beneficial depends on the individual). They reject the idea that certain things can be analyzed on the principle that it is not beneficial or worthwhile to do so. An example of this would be use of socionics in business: although socionics does reflect how people act, actually using it beneficially in a business environment is difficult and overly complex, wasting effort and time on something that might not even make money.

They also do not like concepts or ideals (depending whether they are from Gamma or Delta) that are not practical or reflective of how the world works.” [1]

There are four types of intertype relationships that exist between types of the same quadra:
Mirror, Duality, Activation, and Identity. 

These are considered the most ideal relationships one can have throughout socionics, due to similar interests, preferences, and methods of thought.

References:

[1] https://www.wikisocion.net/en/index.php?title=Quadra