It's the exact idea on which mutual fund houses are functioning and the monthly purchasing is called "SIP". But anyway, why do you want to create a group?
Does that mean, you will first create pool of funds and then buy the bitcoin in one go, and then distribute the proportionate amount of bitcoins to the investment of the group member? Am I understanding it correctly?
It's just a group (actually it's more like just a board) to be able to display crowd activity. If someone sees that many people are doing something they might be more encouraged to do the same thing, too. It's not about facilitating that at all - I don't want your money :-D