Not directly. One of the reasons Jira was written was that "assign to group" does not work in real life. It allows for "someone else was dealing with it", and if you allow that, it inevitably happens. This is bad practice and hence, the assignee should always be a single person.
If you must do this bad thing in plain Jira, then you will need to burn a licence seat with a dummy user who represents the group and has an email address that is translated to a distribution list by your email system.
Service Desk has a better way to handle this as well - instead of assigning to a group, get the group to understand that they have a queue of requests coming in and they are all responsible for them. Then use the queues.
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