Hi,
sorry for late reply, it was a weekend

Unfortunately this is not possible (and we does not want to expose usergroups in frontend), but there is a workaround, you can use a field and set usergroups with conditions based on the value of this field, for example:
- Create a field of type select and add these options:

registered|Registered

author|Author

manager|Manager

administrator|Administrator

- Add conditions like this:
1) if equal to custom value "author" then add to Usergroup "Author"
2) if equal to custom value "manager" then add to Usergroup "Manager"
3) if equal to custom value "administrator" then add to Usergroup "Administrator"
* Note: you does need to add condition for "Registered" usergroup because all registered users should be always in this usergroup