Hum, sim. Isso é o que são as permissões de grupo . A maneira como você configurou agora é:
d rwx rwx r-x
- --- --- ---
| | | |------> Everybody can read(r) and execute(x)
| | |
| | |----------> All group members can read(r), write(w) and execute(x)
| |
| |--------------> Owner can read(r), write(w) and execute(x)
|
|-----------------> it is a directory