To perform Jira's group members export to an .xls format, first be logged as JIRA administrator and then access the visible only to such user cog icon to select "User Management":
The below illustration explains next steps:
After pressing "Export to Excel" you may encounter with the following warning:
Evaluation license only warning.
You have evaluation license - it allows to export only 2 groups. Please purchase full license to be able take full advantage of the Admin Tools for JIRA.