Pigeonhole Principle: splitting into groups

Question

Suppose that there are 51 students in a preschool. The students need to be divided into groups in order to play games. However, each student hates 3 other students, and if A hates B, they cannot be in the same group. What is the smallest number of groups to ensure it always works?

Answer 1

The answer is 2 since if everyone hates persons 1, 2, 3 and 1, 2, 3 don't hate one another it works.