Recognition of the Simple Groups ²D₈((2ⁿ)²)

One of the important problems in finite groups theory is group characterization by specific property. Properties, such as element orders, set of elements with the same order, the largest element order, etc. In this paper, we prove that the simple groups ²D₈((2ⁿ)²)where, 2⁸ⁿ+ 1 is a prime number are uniquely determined by its order and the largest elements order.