  By means of single-crystal X-ray diffraction we have revealed the breaking of
centrosymmetry when lowering the temperature under T$_s$ = 200 K concomitantly
with the setting of a commensurate superstructure in the small A-site quadruple
perovskite YMn$_3$Mn$_4$O$_{12}$. This results is in agreement with all data
already reported for this compounds and solve the previous inconsistency about
the Yttrium position. The superstructure is characterized by the appearing of
satellite reflections in the single crystal pattern, consistent with an
I-centered pseudo-orthorhombic commensurate supercell with $a \approx
\sqrt{a_F} = 10.4352(7)$ \AA, $b \approx 2b_F = 14.6049(9)$ \AA, $c \approx
\sqrt{c_F} = 10.6961(7)$ \AA and $\beta = 90.110(3)^\circ$, where F stands for
the "fundamental" high-temperature cell ($a_F \approx c_F \approx 7.45$ \AA,
$b_F \approx 7.34$ \AA, and $\beta \approx 90^\circ$). The space-group was
unequivocally found to be Ia, which is non polar, thus allowing for a non-zero
polarization in the material. We then have investigated in detail the
pyrocurrent, transport, dielectric and the DC and AC magnetic properties of
polycrystalline sample of YMn$_3$Mn$_4$O$_{12}$ over a wide temperature range.
These measurements clearly highlight several critical temperatures in the
material and correlation between the different orders: i) the centrosymmetry is
broken at high temperature (T$_S$ = 200K), ii) then the long-range magnetic
order of B-sites occurs at T$_{N,B}$ = 108 K and at this same temperature the
compound enters in an insulating dielectric state. iii) Finally, a remnant
polarization is stabilized concomitantly with a magnetic anomaly at T* = 70 K.
We propose that YMn$_3$Mn$_4$O$_{12}$ is a peculiar magnetic ferroelectric in
which the polar state is driven by short-range magnetic order.
