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Given an LCD group code $C$ in a group algebra $KG$, we inspect kinshipbetween $C$ and $G$, more precisely between the subgroup structures of $G$ and$C$. Under some special circumstances our inspection provides an estimation forvarious parameters of a group code $C$. When $C$ is MDS, the inter relationbetween $K$ and $G$ becomes more impressive. Application of Sylow theoremfacilitated us to explore the inter relation between $G$ and $K$ (when $C$ isLCD and MDS) in more general way and finally we get the result of Cruz andWillems (Lemma $4.4$) as a simple sequel.

On maximum distance separable group codes with complementary duals