As you suggested,I have created a role with only one tcode SU01 and for S_USER_GRP I have given in the following way:
Activity: 05
Group name: Test_Group
and assigned this to user(Test1).
We have other groups like Test_Group1,Test_Group2 etc. But User(Test1) still able to do changes for Test_Group1 and T_Group2 rather than Test_Group