such a simple thing to do, often takes me a hard time to find. if you have a group id, here is how to get the info for that group:
$group = groups_get_group( array( 'group_id' => $group_id ) );
you could also add ‘load_users’ => true in the array if you want the members.
here is an example of the output.
BP_Groups_Group Object ( [id] => 186 [creator_id] => 1 [name] => Featured Stories [slug] => int-times-feature [description] => This group sends out a weekly summary of features stories from the Community News Magazine. If you'd like to receive featured stores notifications more frequently, change your email options to Daily Digest or New Topics. [status] => public [enable_forum] => 1 [date_created] => 2010-08-19 21:03:53 [admins] => Array (  => stdClass Object ( [user_id] => 1 [user_login] => admin [user_email] => email@example.com [user_nicename] => admin [is_admin] => 1 [is_mod] => 0 ) ) [total_member_count] => 4 [last_activity] => 2011-02-24 23:44:06 [is_member] => 1