"group by" is quite expensive

What can I do to speed up queries like the following

select count(*) from ttt group by xxx;

Using Postgres 7.1 on Solaris 8 the above query on a 1M row
database takes 6 times longer than the following

select count(*) from ttt;

With Postgres "group by" is apparently quite expensive. Using
Oracle and MySQL the same query and the same data, the first query
takes only 25% longer. I think both of these DBMSes use a single
sequential scan of the data while Postgresql (using the explain query)
uses a multi pass process. Yes I did a vacuum analyze.

Is there anything I as user can do. Build some kind of index?

In absolut times "group by" is a killer. All querries on a single
1M row table that include "group by" take about 3 minutes. Oracle
takes about 40 seconds and MySQL about 25 seconds.

Here is what EXPLAIN shows.

alberch=# explain select count(*) from tyc_main group by nphoto;
NOTICE: QUERY PLAN:

Aggregate (cost=170404.22..175695.88 rows=105833 width=2)
-> Group (cost=170404.22..173050.05 rows=1058332 width=2)
-> Sort (cost=170404.22..170404.22 rows=1058332 width=2)
-> Seq Scan on tyc_main (cost=0.00..49705.32 rows=1058332
width=2)

EXPLAIN
alberch=# explain select count(*) from tyc_main;
NOTICE: QUERY PLAN:

Aggregate (cost=52351.15..52351.15 rows=1 width=0)
-> Seq Scan on tyc_main (cost=0.00..49705.32 rows=1058332 width=0)

EXPLAIN

When I run the queries the last takes 18 sec, the first
a little over 5 _minutes_