168 — The Hours in a Week and a Hidden Group

168 = 7 × 24, the number of hours in a week. But 168 has deeper significance: it is the order of PSL(2,7), the smallest non-abelian simple group after A₅ (which has order 60). This group acts on 7 points with remarkable symmetry and appears in the study of the Klein quartic — a Riemann surface tiled by 24 heptagons with the maximum possible symmetry for its genus. The number 168 connects a mundane fact about time-keeping to one of the most beautiful objects in all of mathematics.