Question

give an example of non cyclic group?

Answer 1

Answer:

Problem: Find an example of a noncyclic group, all of whose proper subgroups are cyclic. ... The group U(8) = 11,3,5,7l is noncyclic since 11 = 32 = 52 = 72 = 1 (so there are no generators). The only proper subgroups are 11l, 11,3l, 11,5l, and 11,7l, which are all obviously cyclic. 14.