Both intelligent reflecting surface (IRS) and non-orthogonal multiple access (NOMA) are considered as potential techniques for the next-generation mobile communication system. In this paper, we concentrate on the power minimization problem for a multi-antenna IRS-NOMA uplink system, which is addressed by alternatively optimizing transceivers and phase shifts. Particularly, the users are divided into one central group and one edge group according to their propagation distances to the base station, where the data transmission of the edge group is assisted by the IRS. Besides, from the perspective of practice, a non-ideal group-based successive interference cancellation (GSIC) is taken into account. To proceed, an iterative algorithm with the minimum mean square error equalizer is leveraged to design the transceivers and a sequential rotation algorithm is developed to optimize the phase shifts. Simulation results indicate the superiority of the proposed scheme compared with various benchmarks in terms of transmit power consumption.