168 (number)

168 is the natural number following 167 and preceding 169.

It is the sum of four consecutive primes (37 + 41 + 43 + 47).

There are 168 primes less than 1000.

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).

One hundred sixty-eight is also:

• The year AD 168 or 168 BC.
• The number of hours in a week.
• The total number of pips on a standard domino set.

References

• This Week's Finds in Mathematical Physics 214, John Baezcv:168 (хисеп)

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