In general a n -rotation group, [2 p 1,2,2 p 2,2,..., p n ] may require up to n generators if gcd(p 1,.., p n)>1, as a product of all mirrors, and then swapping sequential pairs. The half group, [2 p 1,2,2 p 2,2,..., p n ] has generators squared. n -rotary reflections are similar.