Hi there,
I had a pop at this, and ended up with a solution that's a bit too much like line noise. Anyway, here you go:

#!/usr/bin/perl

use warnings;
use strict;

#Your data, I messed with the Group attribute to test my code.

my $hoh = {

        '1018884184639' => {
                'Group' => 'Marketing',
                'System Name' => '1018884184639',
                'Authorization' => 'mrossa'
        },

        '1017939213033' => {
                'Group' => 'Marketing',
                'System Name' => '1017939213033',
                'Last Update' => 'Thu Apr 18 14:29:30 2002',
                'Support Tools' => 'EGstools',
                'Source Code Management' => 'EGscm',
                'Production Platforms' => 'EGpp',
                'Design Tools' => 'EGdest',
                'Authorization' => 'dsmith',
                'Test Tools' => 'EGtt',
                'Database' => 'EGdb',
                'URL' => 'http://www.perlmonks.com',
                'Middleware' => 'EGmidd',
                'Database Tools' => 'EGdb',
                'Found Internal Libraries' => 'EGfdxi',
                'Development Languages' => 'EGdl',
                'Development Tools' => 'EGdtools',
                'Fail Over Software' => 'EGfos'
        },

        '1017939028902' => {
                'Group' => 'Shipping',
                'System Name' => '1017939028902',
                'Last Update' => 'Fri Mar 29 10:32:44 2002',
                'Support Tools' => '9',
                'Source Code Management' => '10',
                'Production Platforms' => '1',
                'Design Tools' => '12',
                'Authorization' => 'ecartman',
                'Test Tools' => '11',
                'Database' => '4',
                'URL' => 'http://www.osdncom',
                'Middleware' => '2',
                'Database Tools' => '5',
                'Found Internal Libraries' => '7',
                'Development Languages' => '6',
                'Development Tools' => '8',
                'Fail Over Software' => '3'
        },
};


#We have a hash of system hashes, and we want to sort/group by the key
+s within
#the system hashes.

#First, find out what attributes you're going to sort/group by
my %sorted_by_attribute;

#Loop through all the systems
foreach my $system (keys %$hoh) {


        #Loop through all the keys found within each system, eg 'Devel
+opment Tools'
        foreach my $attribute (keys %{$hoh->{$system}}) {


                #Get the value of that key, eg '8', and push the syste
+m name onto
                #an array which is unique to that attribute, then the 
+value of that attribute

                my $attribute_value = $hoh->{$system}{$attribute};
                push @{$sorted_by_attribute{$attribute}{$attribute_val
+ue}}, $system;


                #Offhand, $sorted_by_attribute{$attribute}{$attribute_
+value} is an array reference,
                #hence the deref'ing curlies and @ symbol. (You can't 
+put a straight array into
                #a hash)


        }



}

#Now %sorted_by_attributes looks like this:
#$VAR1 = {
#          'Group' => {
#                       'Marketing' => [
#                                        '1017939213033',
#                                        '1018884184639'
#                                      ],
#                       'Shipping' => [
#                                       '1017939028902'
#                                     ]
#                     },
#       .
#       .
#       .
#       }


#Print the data
foreach my $attribute (sort keys %sorted_by_attribute) {
        my $individual_values = $sorted_by_attribute{$attribute};

        print $attribute, "\n";
        foreach my $value (keys %$individual_values) {
                my @systems = @{$sorted_by_attribute{$attribute}{$valu
+e}};
                print $value, " := ";
                print join ", ", @systems;
                print "\n";
        }
        print "\n";

}
[download]

Blech.
Hopefully the comments are enough to allow you to understand it
cheers

davis
Is this going out live?
No, Homer, very few cartoons are broadcast live - it's a terrible strain on the animator's wrist
Update: Fixed missing octothorp for comment. D'oh.