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Context. Although heavily obscured active galactic nuclei (AGNs) have been found by many observational studies, the properties of the surrounding dust are poorly understood. Using AKARI/IRC spectroscopy, we discover a new sample of a heavily obscured AGN in LEDA 1712304 which shows a deep spectral absorption feature due to silicate dust. Aims. We study the infrared (IR) spectral properties of circumnuclear silicate dust in LEDA 1712304. Methods. We perform IR spectral fitting, considering silicate dust properties such as composition, porosity, size and crystallinity. Spectral energy distribution (SED) fitting is also performed to the flux densities in the UV to sub-millimeter range to investigate the global spectral properties. Results. The best-fit model indicates 0.1 $\mu$m-sized porous amorphous olivine (${\rm Mg_{2x}Fe_{2-2x}SiO_4}$; $x=0.4$) with $4\%$ crystalline pyroxene. The optical depth is $\tau_{\rm sil}{\sim}2.3$, while the total IR luminosity and stellar mass are estimated to be $L_{\rm IR}=(5\pm1){\times}10^{10}\,L_{\odot}$ and $M_{\rm star}=(2.7\pm0.8){\times}10^{9}\,M_{\odot}$, respectively. In such low $L_{\rm IR}$ and $M_{\rm star}$ ranges, there are few galaxies which show that large ${\tau}_{\rm sil}$. Conclusions. The silicate dust in the AGN torus of LEDA 1712304 has properties notably similar to those in other AGNs as a whole, but slightly different in the wing shape of the absorption profile. The porosity of the silicate dust suggests dust coagulation or processing in the circumnuclear environments, while the crystallinity suggests that the silicate dust is relatively fresh., Comment: 9 pages, 6 figures, accepted for publication in A&A