The definitions I see for group all use "a number",e.g. "a number of people or things that are located, gathered, or classed together". So if you're willing to accept 1 as a possible value for a number, it's not an oxymoron.

Is 0 people a group by the unusual definition you use?

It is, at least in principle. As I see it, there's nothing that immediately discontinues a group when the last person leaves; it only makes it inactive. But a group could also become inactive in many other ways (e.g. deciding not to meet for a long time). It's only if whatever organization that found a benefit at having that group, no longer does and decides to discontinue it, then it stops being a group.

What a weird world you live in. What about "the organization"? What if it has 0 people?

The world I live in is one which accepts both usual and unusual circumstances.

In the extreme case, consider a small company whose few owners and employees suddenly pass away (e.g. in a plane crash). The fact that the company suddenly has 0 employees and even 0 shareholders does not immediately terminate the company. It still continues to exist as a business and legal entity, until the government / lawyers either find new shareholders (typically heirs) who are willing to run the company, or appoint a director to initiate foreclosure.

1+1=1

0 × 0 = 0

A single item list is still a list.