Are there actions which are morally permissable when undertaken by a group but which would be immoral if performed by an individual?
An important philosophical consideration here before you get going on this issue is deciding what you mean by a group. In particular, you might consider whether you buy into what's been called methodological holism which means here, basically, that the whole is more than the sum of its parts. So, an economic class, a nation, a people, a family is more than just the individuals that compose it. Methodological individualism holds just the opposite, namely that the whole is nothing more than the sum of the parts. Would you say that the state is a group? Then, certainly, there are things that this group can do that would be immoral if performed by an individual. For example: imprison people, judge and punish criminals, conduct wars, appropriate property and tax, marry, etc.