  We construct a generalized Darboux transformation (GDT) of a general coupled
nonlinear Schr\"{o}dinger (GCNLS) system. Using GDT method we derive a
recursive formula and present determinant representations for N-th order rogue
wave solution of this system. Using these representations we derive first,
second and third order rogue wave solutions with certain free parameters. By
varying these free parameters we demonstrate the formation of triplet, triangle
and hexagonal patterns of rogue waves.
