  Layered intermetallic compounds with kagom\'e lattices provide access to the
electronic structures and exotic phenomena associated with flat bands and
Dirac-type dispersion that are enforced by atomic connectivity. Here, we report
the preparation of ~ 20 mm x 50 mm single crystals of MgCo$_6$Ge$_6$ via laser
Bridgman growth. X-ray precession images and electron diffraction measurements
show MgCo$_6$Ge$_6$ crystallizes in space group \textit{P6/mmm}, with a =
5.06094(15) \r{A}, c = 7.7271(2) \r{A}. The structure, solved at T = 293(2) K,
consists of eclipsed Co kagom\'e and hexagonal Ge layers with Mg and (Ge$_2$)
dimers filling the hexagonal channels. Residual electron density maps provide
evidence of Ge-Ge disorder along the c axis. Magnetization measurements
indicate Pauli paramagnetic behavior with a crystalline anisotropy developing
below T $\approx$ 20 K. Resistivity data show a metallic temperature
dependence, with evidence of an electron-electron scattering driven
contribution of A = 58(13)*10$^{-5}$ m$\Omega$.cm.K$^{-2}$. Specific heat
measurements show a low temperature electronic contribution of $\gamma$ =
20.84(28) mJ.K$^{-2}$.mol$^{-1}$. The Kadowaki-Woods ratio is
0.134(21)*10$^{-2}$ $\mu\Omega$.cm.mol$^{2}$.K$^{2}$.mJ$^{-2}$, comparable to
hexagonal layered Na$_{0.7}$CoO$_2$ and strongly enhanced Wilson ratio of
$\approx$ 7.7 - 5.2 similar to strongly correlated layered cobalt oxide
[BiBa$_{0.66}$K$_{0.36}$O$_2$]CoO$_2$. Analysis of the phonon density of states
extracted from specific heat shows the existence of a low-lying Einstein-like
contribution (T$_{op}$ = 121.41(47) K), a feature absent in the related
compounds YCr$_6$Ge$_6$ and LuFe$_6$Ge$_6$. Our results add to the knowledge of
kagom\'e metals and suggest directions for future exploration to connect
structural and electronic behaviors in these fascinating materials.
