These are some random examples of groups:

• Continuous groups
  1. Z,+ infinite abelian
  2. Z,* not a group. violates inverse
  3. R,* not a group. violates inverse for 0
  4. R,+ infinite abelian
  5. R*=R-{0},* infinite abelian
  6. R*=R-{0},+ not a group. violates identity
• Finite groups
  1. {e} order 1
  2. cyclic group
  3. dihedral group
  4. Z mod n,+
• Conjugacy classes