clause?

Sounds like an introductory clause.

What's the rest of the sentence?

No, it's a prepositional phrase. Without the word 'in,' it could be a noun phrase.

You really DO need to give us the context of your clause.

Samples:

In a society characterized by homogeneity, we ought to figure out our problems.

I don't want to live in a society characterized by homogeneity.

She wanted to live in the Amazon, in a society characterized by homogeneity.