I am computing the second cohomology group $H^2(G,\mathbb{Z_3})$ of $G=$SmallGroup(81,9). Its presentation is given by $G=\langle x,y,z\mid x^3=y^9=z^3=[y,z]=1,[y,x]=z,[z,x]=zy^3z^{-1}\rangle$. I tried using the Consistency test (Alexander Wegner's PhD Thesis, Theorem 2.7, page-23). From My calculations, I am getting $H^2(G,\mathbb{Z_3})\cong \langle (1,0,0,0,0,0),(0,0,1,0,0,0),(0,0,0,0,1,0)\rangle$. But Gap computations show that $H^2(G,\mathbb{Z_3})\cong {\mathbb{Z_3}\times \mathbb{Z_3}\times \mathbb{Z_3}\times \mathbb{Z_3}}$.
Can Anyone help me where I am making a mistake? I have checked it many times. I am attaching a link to my Calculations.
Thank you very much in advance.