In this paper, we show that the Picard modular group \({PU}(2, 1; \mathcal {O}_7)\) can be generated by five explicitly given transformations. First using the Langlands decomposition we will see that three Heisenberg translations together with a Heisenberg rotation generate the stabilizer subgroup of infinity. Then through a geometric argument and also an algebraic argument we show that adjoining an inversion to the transformations described previously generates \(PU(2, 1; \mathcal {O}_7).\) The idea behind the geometric method is finding a union of isometric spheres such that a fundamental domain for the stabilizer subgroup of infinity lies inside their boundaries. And the idea behind the algebraic method is to implement the continued fraction algorithm.
