What is the legal definition of a hate crime? Is this definition sufficient?

What is the legal definition of a hate crime? Is this definition sufficient? How would you change it, if at all? Also, define right-wing extremism and left-wing extremism. What is an example of a left-wing group? What is an example of a right-wing group? How does each group use the Internet to carry out their nefarious activities? What tools does law enforcement have to combat these groups? Should be at least 200 words in length.