Explore the fascinating world of hypergroups and their connection to symmetry in this 41-minute lecture on the square lattice and group D4. Delve into the importance of Bravais lattices in chemistry, physics, and mathematics, focusing on the square lattice's symmetry. Examine the classical view of the square lattice space group, involving both the point group D4 and a lattice normal subgroup. Discover the character table of the finite group D4 and its associated class and character hypergroups. Uncover remarkable orthogonality relations for both rows and columns of the hypergroup character table, providing powerful tools for harmonic analysis in symmetry-ruled situations. Learn how this connects to the discussion of Dihedrons and gain insights into the broader applications of these concepts in mathematics and related fields.