Email for any alerts triggered on devices within a group.

You could add a custom property to the groups, and have it be a list of emails to notify. I detailed that out here a bit: Help with Alerting on Node & Group

Another way which is similar, apply the same custom property (of emails to notify) to all nodes in that group. Inside the custom property editor, you can actually sort your nodes by group so it makes that suuuuuper easy. Then you could utilize a node alert which I tend to prefer.

Check out this thread about the custom properties used for emailing in alerts. Using Custom Properties sending Alert emails

The first example will only send an alert if the node is down which I've already figured out how to do based on group.  I've got an alert setup based on group, using group member.  However, I'm looking for something to trigger an email to a specific team if a device happens to trigger any alerts.  At times there may be several teams that have the same device within their group, so I'd prefer this to be some sort of alert triggered based on the group rather than having to set custom properties for thousands of devices.

You can also alert if the group goes into warning status as well. Though, I understand your need. I can't think of any way to currently do that unless utilizing a custom SQL, or SWQL query. If you adjust your alerts to use custom properties for email, I think that'd be the easiest way to achieve this. Rather than alert on alerts (probably more of a reporting function)... simply have the alerts emailed directly to the teams that own the devices. Then they could take action immediately. You can use multiple custom properties, and CC/BCC etc. I believe.