A group center subgroup and derived subgroup are two important normal subgroups. The article mainly focuses on the third and fourth-order unit upper triangular matrix group. We obtain the center of group of the third-order unit upper triangular matrix group agrees with its derived group, whereas the conclusion is false in the forth-order unit upper triangular matrix group.%群的中心和导群是两个重要的正规子群，主要讨论了三阶和四阶单位上三角矩阵群的导群与中心，得到了三阶单位上三角矩阵群的导群与中心相等，而四阶不等。
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