What is an example of a cyclic group with exactly 6 generators?

Question

Hi I need an example of a cyclic group with exactly 6 generators, thank you.

Answer 1

If it has $6$ generators, and since $e$ is never a generator (unless it's the trivial group, which it's not), then the group you are looking for must have at least $7$ elements. How many cyclic groups with $7$ elements do you know? (hint: essentially just one.) For that single most immediate candidate as an answer, is it true that each of its elements other than $e$ is a generator? (Hint: the order of an element in a cyclic group is easy to compute. What do you know about it?)