#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my $group   = shift;
my $gid     = getgrnam $group;
my @members = split ' ', (getgrgid $gid)[-1];

say "<$_>" for @members;

while (my ($pwnam, $group_id) = (getpwent)[0, 3]) {
    say "[$pwnam]" if $group_id == $gid;
}
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(Angle and square brackets added to emphasize the origins of the information)

Nice solution; personally I prefer the OO User::pwent and User::grent:

use warnings;
use strict;
use feature qw/say/;
use User::grent;
use User::pwent;

my $grnam = shift;
die "Usage: $0 GROUPNAME\n" unless length $grnam;
my $group = getgrnam $grnam;
die "Group '$grnam' not found\n" unless defined $group;

say "<$_>" for @{$group->members};

while ( my $pwent = getpwent ) {
    say "[",$pwent->name,"]" if $pwent->gid == $group->gid;
}
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Thanks! getgrgid was the function I needed:

my $gid     = getgrnam $group;
my @members = split ' ', (getgrgid $gid)[-1];
[download]

I now see where getgrgid is in the function manual, perlfunc(1). I'll have to read through that section until I get it.