how about this:

($firstLetter)= ($file_name=~ /^(.)/);
push(@{$hash{uc($firstletter)}}, $infoline);
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This will give you a hash of arrays:

$hash{'A'} -> [ infolineA1, infolineA2 ... ]
$hash{'B'} -> [ infolineB1, infolineB2 ... ]
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with this loop

foreach $letter (sort keys %hash) {
    print $letter;
    foreach $infoline (@{$hash{$letter}}) {
        print $infoline;
    }
}
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you can output your lists. Note that I've added a uc() to $firstletter above, giving you just upper case.

This might not be the best way to do it, but its at least one way.