TITLE: Automorphism in Z7
QUESTION [6 upvotes]: how many automorphisms are there in  Z7?
Z7={0,1,2,3,4,5,6}
 Identity and inverse are two automorphisms I found.

REPLY [3 votes]: $\text{Aut }\mathbb Z_7\simeq U_7=\{1,2,3,4,5,6\}.$ So there are $6$ such automorphisms.