Let $G$ be a finite group. The degree pattern of $G$ denoted by $D(G)$ is defined as follows: If $\pi(G)=\{p_{1},p_{2},...,p_{k}\}$ such that $p_{1}<p_{2}<...<p_{k}$, then $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where $deg(p_{i})$ for $1\leq i\leq k$, are the degree of vertices $p_{i}$ in the prime graph of $G$. In this article, we consider a finite group $G$ under assumptions $|G|=|L_{4}(2^{n})|$ and $D(G)=D(L_{4}(2^{n}))$, where $n\in\{5, 6, 7\}$ and we prove that $G\cong L_{4}(2^{n})$.
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