168 (number)

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168 is the natural number following 167 and preceding 169.

List of numbers — Integers << 160 161 162 163 164 165 166 167 168 169 >>
Ordinal	One hundred [and] sixty-eight
Cardinal	168th
Factorization
Roman numeral	CLXVIII
Binary	10101000
Hexadecimal	A8

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

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.

[edit] References

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