Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi>ϕ</mml:mi><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>at BESIII

Based on a sample of $2.25\ifmmode\times\else\texttimes\fi{}{10}^{8}J/\ensuremath{\psi}$ events taken with the BESIII detector at the BEPCII collider, we present the results of a study of the decay $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. The $Y(2175)$ resonance is observed in the invariant mass spectrum of $\ensuremath{\phi}{f}_{0}(980)$ with a statistical significance of greater than $10\ensuremath{\sigma}$. The corresponding mass and width are determined to be $M=2200\ifmmode\pm\else\textpm\fi{}6(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}5(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and $\mathrm{\ensuremath{\Gamma}}=104\ifmmode\pm\else\textpm\fi{}15(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}15(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}$, respectively, and the product branching fraction is measured to be $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\eta}Y(2175),\phantom{\rule{0ex}{0ex}}Y(2175)\ensuremath{\rightarrow}\ensuremath{\phi}{f}_{0}(980),{f}_{0}(980)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(1.20\ifmmode\pm\else\textpm\fi{}0.14(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.37(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. The results are consistent within errors with those of previous experiments. We also measure the branching fraction of $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{f}_{1}(1285)$ with ${f}_{1}(1285)\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and set upper limits on the branching fractions for $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\eta}(1405)/\ensuremath{\phi}X(1835)/\ensuremath{\phi}X(1870)$ with $\ensuremath{\eta}(1405)/X(1835)/X(1870)\ensuremath{\rightarrow}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ at the 90% confidence level.