Abstract: In [1, 1.9], Shi defined a congruent relation on the set of all presentations of a finite complex reflection groups G. Shi also gave all the non-congruent presentations of G with G∈{G₁₂, G₂₄,G₂₅, G₂₆} and proved that all those presentations he gave are essential[1, 7.1]. In this paper, we found all the non-congruent essential presentations of G₂₇.

Key words: congruent presentation, essential presentation, complex reflection group, presentation, congruent presentation, essential presentation, complex reflection group