Grouping and Transposing Rows to Columns in PostgreSQL

I have the follwing situation: I have profiles and tasks. One profile can be used once for each task. I track usage in profiles_used table. I need to build a report that shows how many profiles of each group is available for each task.

Here are my tables:

select * from profiles;

 id |  name   | group
----+---------+---------
  1 |  name_1 | 1
  2 |  name_2 | 2
  3 |  name_3 | 3
  4 |  name_4 | 3
  5 |  name_5 | 3


select * from tasks;

 id | name
----+--------
  1 | task_1
  2 | task_2
  3 | task_3


select * from profiles_used;

 id | task.id | profile.id
----+---------+------------
  0 | 1       | 1
  1 | 1       | 2
  2 | 2       | 1
  3 | 3       | 4
  3 | 3       | 5

Magic: Run query that finds out how many not used profiles in each group available for each task.

Result:

             profiles.group
 task.id |  1  |  2  |  3  
---------+-----+-----+-----
       1 |  0  |  0  |  3
       2 |  0  |  1  |  3
       3 |  1  |  1  |  1

Please help me with right direction to start.