Millimeter-wave technology provides the necessary improvements in capacity and performance for the next generation of wireless networks. The new IEEE 802.11ay amendment extends IEEE 802.11ad to offer 100 Gbit/s connectivity in the unlicensed 60 GHz band through technical advancements such as Multiple-Input and Multiple-Output (MIMO), channel bonding and aggregation. Additionally, it offers improvements to the Beamforming Training (BFT) process in order to increase its efficiency and accuracy. One new technique defined by IEEE 802.11ay is Group Beamforming, which allows to simultaneously train all stations, and significantly reduces training overhead, especially in very dense networks. In this paper, we provide an implementation of IEEE 802.11ay in ns-3 and perform, to the best of our knowledge, the first detailed system-level evaluation of the performance of the novel IEEE 802.11ay protocol. We specifically study the performance of Group Beamforming and compare it against the legacy 802.11ad BFT. We explore how different BFT approaches scale in large networks, identify the possible problems and evaluate at how the BFT process influences the performance of the network overall. Our analysis shows that Group Beamforming can outperform the legacy approach, resulting in lower overhead and improved network performance. However, we also found that the Access Point (AP) training is quite vulnerable to interference in dense networks, introducing severe limitations to the performance, especially in large rooms where precise BFT is crucial to maintain the communication link. Therefore, we propose several improvements to Group Beamforming that improve performance and provide robust beamforming even in very dense scenarios.