This will most likely require using an SQL macro in the trigger action. What types of objects are going in as group members? Just nodes?
As the others have suggested,
The default 'Alert me when a group goes down' and 'Alert me when a group goes into a warning or critical status' will suffice here. If you have all members down, the group status will be down regardless of which group status you chose (Best, mixed mode, worst). The test function doesn't allow you to select a Group, it only allows you to select a node. That's probably why the Test isn't working as you expect but these are the alerts you need to use for sure.
2 Alerts per group. One for the All Members down, and one for Less than all down (at least 1).
X # of Group x 2 Alerts Per Group = 2X Alerts.