  Structural, magnetization, phonon behavior, and dielectric response of
nano-crystalline Gd$_2$CoMnO$_6$ have been presented in this paper. The study
shows that the material crystallizes in $\textit{P2$_1$/n}$ phase group of the
monoclinic crystal structure. XPS measurement shows Co$^{2+}$ and Mn$^{4+}$
oxidation states are present in the sample. Magnetization study reveals that
the sample undergoes a ferromagnetic ordering of Co$^{2+}$ and Mn$^{4+}$
magnetic ions around $T_c$ $\sim$132 K. However we have seen that with the
application of external magnetic field the phase transition is largely
suppressed. Raman study reveals the presence spin-phonon coupling in
Gd$_2$CoMnO$_6$. Dielectric study reveals that the sample shows large
dielectric constant and strong dispersion in mid frequency range. The
dielectric loss shows there are two relaxation processes present in the
material with different relaxation time and which are driven by thermally
activated relaxation mechanics. Further, the Nyquist plot and AC conductivity
study show that this sample is non-Debye's in nature.
