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We prove that the $3$-group of order $3^{84}$ introduced by Abdollahi, Faghihi, and Mohammadi Hassanabadi, and later shown by Abdollahi, Faghihi, Linton, and O'Brien to have the corresponding automorphism property, is an E-group. Let $P$ denote this group and put $V=P/\\Phi(P)\\cong \\mathbb{F}_3^9$. The nine power relations of $P$ determine a linear map $q:V\\longrightarrow\\Lambda^2 V$. 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