So when you need to JOIN Tables, you have to use rawQuery instead of query.
So your statement
String SELECT_QUERY = SELECT * FROM Table1 t1 INNER JOIN Table2 t2 ON t1.id = t2.id GROUP BY t1.data1;
I recommend to you use JOIN because it more faster and safer then your approach. So then your rawQuery method can looks like this:
cursor = db.rawQuery(SELECT_QUERY, null);
Have look at
rawQuery in SQLiteDatabase
Regards