  Structural and magnetic properties of the CoMn$_{0.88}$Cu$_{0.12}$Ge compound
have been investigated using X-ray diffraction (XRD) and differential scanning
calorimetry (DSC) accompanied with investigation of magnetic properties under
applied hydrostatic pressure up to 12 kbar. It has been found that the
orthorhombic crystal structure of the TiNiSi-type, which is dominant at low
temperatures, turns into the hexagonal Ni$_2$In-type one, slightly above 200 K.
The structural transition is of the first-order type as confirmed by presence
of distinct thermal hysteresis exceeding 20 K. The ac magnetic measurements
indicate a ferromagnetic order below the Curie temperature $T_C$ of 238 K,
followed by additional anomaly at lower temperatures - the latter one being
related to the structural transition. Application of hydrostatic pressure leads
to temperature separation of the purely magnetic transition, whose Curie
temperature $T_C$ slowly increases with applied pressure, and the
magnetostructural transition characterized by critical temperature showing much
rapid decrease with increasing pressure. Comparison of the DSC data for the
investigated compound and the isostructural CoMn$_{0.95}$Cu$_{0.05}$Ge one has
made it possible to determine both the structural and magnetic components of
entropy change.
