168?

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Years: 164 165 166 167 - 168 - 169 170 171 172

Decades: 130s 140s 150s - 160s - 170s 180s 190s

Centuries: 1st century - 2nd century - 3rd century

Have to see

Contents 1 Mathematics 2 Events 3 Births 4 Deaths 5 Other 6 Meanings/Interpretation 7 References

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Mathematics

168 is the order of the group PSL(2,7), the second smallest nonabelian simple group. From Hurwitz's automorphisms theorem we know that 168 is the maximum possible number of automorphisms of a genus 3 Riemann Surface, this maximum being achieved by the Klein quartic, whose symmetry group is PSL(2,7). The Fano plane has 168 symmetries, and again the symmetry group is PSL(2,7).

Events

• Change of Han Huandi to Han Lingdi of Han Dynasty; first year of Jianning era.

Births

• Zhao Yun, a commander of the civil wars of the late Han Dynasty and the Three Kingdoms period of China (died in 229)
• Jiang Qin, an officer in the kingdom of Wu during the Three Kingdoms period of China. He died in 213 A.D.

Deaths

• Han Huandi, emperor of Han Dynasty

Other

There are 168 hours in a week

Meanings/Interpretation

In the Chinese culture, "168" is regarded as a highly successful number. In Cantonese, "168," read "yut look baat," which sounds similar to "a road of good fortune." This belief has inspired many Chinese to find ways of embedding this number in any possible way, including house numbers, phone numbers, and vehicle license plates.

References

• This Week's Finds in Mathematical Physics 214, John Baez

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