This paper examine certain behavior of some permutation statistics on the pattern ωi defined by Garba and Ibrahim ([GI09]). We investigate the permutation statistics that are equidistributed on ωi∈Gp for any prime p≥5. This to a larger extent helped in identifying ωi as an Eulerian distribution. The graph permutation of ωi and the graph of 132-avoiding pattern of ωi were also studied.