In this paper, we revisit the group recommendation problem, by taking into consideration the information diffusion in a social network, as one of the main criteria that must be maximised. While the well-known influence maximization problem has the objective to select k users (spread seeds) from a social network, so that a piece of information can spread to the largest possible number of people in the network, in our setting the seeds are known (given as a group), and we must decide which k items (pieces of information) should be recommended to them. Therefore, the recommended items should at the same time be the best match for that group's preferences, and have the potential to spread as much as possible in an underlying diffusion network, to which the group members (the seeds) belong. This problem is directly motivated by group recommendation scenarios where social networking is an inherent dimension that must be taken into account when assessing the potential impact of a certain recommendation. We present the model and formulate the problem of influence-aware group recommendation as a multiple objective optimization problem. We then describe a greedy approach for this problem and we design an optimisation approach, by adapting the top-k algorithms NRA and TA. We evaluate all these methods experimentally, in three different recommendation scenarios, for movie, micro-blog and book recommendations, based on real-world datasets from Flixster, Twitter, and Douban respectively. Unsurprisingly, with the introduction of information diffusion as an optimization criterion for group recommendation, the recommendation problem becomes more complex. However, we show that our algorithms enable spread efficiency without loss of recommendation precision, under reasonable latency.