On the Uniqueness of a Group of Order r (r > 1)

This chapter is about certain specific finite groups. Groups of order r 1 ≤ r ≤ 30 are tabulated. It is shown that a group G of order r is unique if, and only if, g.c.d (r, ϕ(r)) = 1, where ϕ is Euler totient. This criterion for the uniqueness of a group of order r is due to Dieter Jungnickel [ 5 ].