15. Show that up to isomorphism exactly two groups consisting of 4 elements exist. In other words, find two non-isomorphic group of order 4 such that every group of order 4 is isomorphic to exactly one of them (this requires some puzzling; consider the possible orders of elements in such a group, and try to construct the possible multiplication tables).

          15. Show that up to isomorphism exactly two groups consisting of 4 elements exist.
In other words, find two non-isomorphic group of order 4 such that every group
of order 4 is isomorphic to exactly one of them (this requires some puzzling;
consider the possible orders of elements in such a group, and try to construct
the possible multiplication tables).