Permutation Groups symmetric group S:all permutations r:列m on-to cyclic group Cn:rotations π=(012…n-1)π(i)=(i+1)modn (012…n-1)》generated by(012..n-1) Dihedral group D:rotations reflections p()=(n-1)-i generated by (012...n-1)and p Permutation Groups symmetric group cyclic group Dihedral group Sn Cn Dn : all permutations : rotations : rotations & reflections ⇡ : [n] 1-1 ￾￾￾! on-to [n] h(012 ··· n ￾ 1)i generated by (012 ··· n ￾ 1) ⇡ = (012 ··· n ￾ 1) ⇡(i)=(i + 1) mod n generated by (012 ··· n ￾ 1) and ⇢(i)=(n ￾ 1) ￾ i ⇢