package PointGroupObject;
use Exporter;
@ISA = qw(Exporter);

#公開したいサブルーチン
@EXPORT = qw();

use strict;
use Sci qw($pi);

#========================================================
# 静的メンバー関数
#========================================================

#========================================================
# 変数取得関数
#========================================================

#========================================================
# コンストラクタ、デストラクタ
#========================================================
sub new
{
	my ($module) = @_;
	my $this = {};
	bless $this;
	return $this;
}

sub DESTROY
{
	my $this = shift;
}

#========================================================
# 一般関数
#========================================================
sub FindPointGroup
{
	my ($this, $pHit, $pMArrays) = @_;

	my @MArrays;
	if(!$pMArrays) {
		@MArrays = $this->GetSymmetryOperationArraysInCartesian();
	}
	else {
		@MArrays = @$pMArrays;
	}
	my @PGArrays = $this->GetPointGroupGenerators();

	my %SymOp;
	for(my $is = 0 ; $is < @MArrays ; $is++) {
		if($pHit->[$is]) {
			$SymOp{$MArrays[$is]->{Name}} = 1;
		}
	}

	for(my $ip = 0 ; $ip < @PGArrays ; $ip++) {
		my $pGen = $PGArrays[$ip]{Generators};
		my $IsHit = 1;
		for(my $ig = 0 ; $ig < @$pGen ; $ig++) {
			if(!$SymOp{$pGen->[$ig]}) {
				$IsHit = 0;
				last;
			}
		}
		return $PGArrays[$ip]{Name} if($IsHit);
	}
	
	return '1';
}

sub GetSymmetryOperationArraysInCartesian
{
	my $sin60  = sin( 60.0 * $pi / 180.0);
	my $cos60  = cos( 60.0 * $pi / 180.0);
	my $sin120 = sin(120.0 * $pi / 180.0);
	my $cos120 = cos(120.0 * $pi / 180.0);

	my @MArrays = (
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0, -1,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "i",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  1,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "mx",
		  'Freedom'  => [0, 1, 1],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0, -1,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "my",
		  'Freedom'  => [1, 0, 1],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0,  1,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "mz",
		  'Freedom'  => [1, 1, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [ 1,  0,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "dxy",
		  'Freedom'  => [1, 1, 1],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0,  0,  1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "dyz",
		  'Freedom'  => [1, 1, 1],
		},
		{ 'Matrix' => [ [ 0,  0,  1, 0],
					    [ 0,  1,  0, 0],
					    [ 1,  0,  0, 0] ],
		  'Name'     => "dzx",
		  'Freedom'  => [1, 1, 1],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0, -1,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "2x",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  1,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "2y",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0, -1,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "2z",
		  'Freedom'  => [0, 0, 1],
		},
#		{ 'Matrix' => [ [-1,  0,  0, 0],
#					    [ 0, -1,  0, 0],
#					    [ 0,  0, -1, 0] ],
#		  'Name'     => "S2x",
#		  'Identical' => 'i',
#		  'Freedom'  => [0, 0, 0],
#		},
#		{ 'Matrix' => [ [-1,  0,  0, 0],
#					    [ 0, -1,  0, 0],
#					    [ 0,  0, -1, 0] ],
#		  'Name'     => "S2y",
#		  'Freedom'  => [0, 0, 0],
#		},
#		{ 'Matrix' => [ [-1,  0,  0, 0],
#					    [ 0, -1,  0, 0],
#					    [ 0,  0, -1, 0] ],
#		  'Name'     => "S2z",
#		  'Identical' => 'i',
#		  'Freedom'  => [0, 0, 0],
#		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  1,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "-2x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0, -1,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "-2y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0,  1,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "-2z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [-1,  0,  1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "2d011",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  0,  1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "2d0-11",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0] ],
		  'Name'     => "2d101",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0, -1, 0],
					    [ 0, -1,  0, 0],
					    [-1,  0,  0, 0] ],
		  'Name'     => "2d-101",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [ 1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "2d110",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, -1,  0, 0],
					    [-1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "2d-110",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [      1,       0,       0,  0],
					    [      0, $cos120,-$sin120,  0],
					    [      0, $sin120, $cos120,  0] ],
		  'Name'     => "3x",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ $sin120,      0, $cos120, 0],
					    [       0,      1,       0, 0],
					    [ $cos120,      0,-$sin120, 0] ],
		  'Name'     => "3y",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [ $cos120,-$sin120,      0, 0],
					    [ $sin120, $cos120,      0, 0],
					    [       0,       0,      1, 0] ],
		  'Name'     => "3z",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [      1,       0,       0,  0],
					    [      0, $cos120, $sin120,  0],
					    [      0,-$sin120, $cos120,  0] ],
		  'Name'     => "3x^2",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [-$sin120,      0, $cos120, 0],
					    [       0,      1,       0, 0],
					    [ $cos120,      0, $sin120, 0] ],
		  'Name'     => "3y^2",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ $cos120, $sin120,      0, 0],
					    [-$sin120, $cos120,      0, 0],
					    [       0,       0,      1, 0] ],
		  'Name'     => "3z^2",
		  'Freedom'  => [0, 0, 1],
		},
		{ 'Matrix' => [ [     -1,       0,       0,  0],
					    [      0, $cos120,-$sin120,  0],
					    [      0, $sin120, $cos120,  0] ],
		  'Name'     => "S3x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $sin120,      0, $cos120, 0],
					    [       0,     -1,       0, 0],
					    [ $cos120,      0,-$sin120, 0] ],
		  'Name'     => "S3y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $cos120,-$sin120,      0, 0],
					    [ $sin120, $cos120,      0, 0],
					    [       0,       0,     -1, 0] ],
		  'Name'     => "S3z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,       0,       0,  0],
					    [      0, $cos120,-$sin120,  0],
					    [      0, $sin120, $cos120,  0] ],
		  'Name'     => "S3x^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$sin120,      0, $cos120, 0],
					    [       0,     -1,       0, 0],
					    [ $cos120,      0, $sin120, 0] ],
		  'Name'     => "S3y^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $cos120, $sin120,      0, 0],
					    [-$sin120, $cos120,      0, 0],
					    [       0,       0,     -1, 0] ],
		  'Name'     => "S3z^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,       0,       0,  0],
					    [      0,-$cos120, $sin120,  0],
					    [      0,-$sin120,-$cos120,  0] ],
		  'Name'     => "-3x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$sin120,      0,-$cos120, 0],
					    [       0,     -1,       0, 0],
					    [-$cos120,      0, $sin120, 0] ],
		  'Name'     => "-3y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$cos120, $sin120,      0, 0],
					    [-$sin120,-$cos120,      0, 0],
					    [       0,       0,     -1, 0] ],
		  'Name'     => "-3z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,       0,       0,  0],
					    [      0,-$cos120,-$sin120,  0],
					    [      0, $sin120,-$cos120,  0] ],
		  'Name'     => "-3x^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $sin120,      0,-$cos120, 0],
					    [       0,     -1,       0, 0],
					    [-$cos120,      0,-$sin120, 0] ],
		  'Name'     => "-3y^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$cos120,-$sin120,      0, 0],
					    [ $sin120,-$cos120,      0, 0],
					    [       0,       0,     -1, 0] ],
		  'Name'     => "-3z^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0,  0, -1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "4x",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0,  1, 0],
					    [ 0,  1,  0, 0],
					    [-1,  0,  0, 0] ],
		  'Name'     => "4y",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "4z",
		  'Freedom'  => [0, 0, 1],
		},
		{ 'Matrix' => [ [ 1,  0,  0, 0],
					    [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0] ],
		  'Name'     => "4x^3",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0, -1, 0],
					    [ 0,  1,  0, 0],
					    [ 1,  0,  0, 0] ],
		  'Name'     => "4y^3",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [-1,  0,  0, 0],
					    [ 0,  0,  1, 0] ],
		  'Name'     => "4z^3",
		  'Freedom'  => [0, 0, 1],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  0, -1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "S4x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0],
					    [-1,  0,  0, 0] ],
		  'Name'     => "S4y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "S4z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0] ],
		  'Name'     => "S4x^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0, -1, 0],
					    [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0] ],
		  'Name'     => "S4y^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [-1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "S4z^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0] ],
		  'Name'     => "-4x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0, -1, 0],
					    [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0] ],
		  'Name'     => "-4y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [-1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "-4z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-1,  0,  0, 0],
					    [ 0,  0, -1, 0],
					    [ 0,  1,  0, 0] ],
		  'Name'     => "-4x^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0,  1, 0],
					    [ 0, -1,  0, 0],
					    [-1,  0,  0, 0] ],
		  'Name'     => "-4y^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, -1,  0, 0],
					    [ 1,  0,  0, 0],
					    [ 0,  0, -1, 0] ],
		  'Name'     => "-4z^3",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [      1,      0,      0,  0],
					    [      0, $cos60,-$sin60,  0],
					    [      0, $sin60, $cos60,  0] ],
		  'Name'     => "6x",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ $sin60,      0, $cos60, 0],
					    [      0,      1,      0, 0],
					    [ $cos60,      0,-$sin60, 0] ],
		  'Name'     => "6y",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [ $cos60,-$sin60,      0, 0],
					    [ $sin60, $cos60,      0, 0],
					    [      0,      0,      1, 0] ],
		  'Name'     => "6z",
		  'Freedom'  => [0, 0, 1],
		},
		{ 'Matrix' => [ [      1,      0,      0,  0],
					    [      0, $cos60, $sin60,  0],
					    [      0,-$sin60, $cos60,  0] ],
		  'Name'     => "6x^5",
		  'Freedom'  => [1, 0, 0],
		},
		{ 'Matrix' => [ [ $sin60,      0, $cos60, 0],
					    [      0,      1,      0, 0],
					    [ $cos60,      0,-$sin60, 0] ],
		  'Name'     => "6y^5",
		  'Freedom'  => [0, 1, 0],
		},
		{ 'Matrix' => [ [ $cos60, $sin60,      0, 0],
					    [-$sin60, $cos60,      0, 0],
					    [      0,      0,      1, 0] ],
		  'Name'     => "6z^5",
		  'Freedom'  => [0, 0, 1],
		},
		{ 'Matrix' => [ [     -1,      0,      0,  0],
					    [      0, $cos60,-$sin60,  0],
					    [      0, $sin60, $cos60,  0] ],
		  'Name'     => "S6x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $sin60,      0, $cos60, 0],
					    [      0,     -1,      0, 0],
					    [ $cos60,      0,-$sin60, 0] ],
		  'Name'     => "S6y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $cos60,-$sin60,      0, 0],
					    [ $sin60, $cos60,      0, 0],
					    [      0,      0,     -1, 0] ],
		  'Name'     => "S6z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,      0,      0,  0],
					    [      0, $cos60, $sin60,  0],
					    [      0,-$sin60, $cos60,  0] ],
		  'Name'     => "S6x^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $sin60,      0, $cos60, 0],
					    [      0,     -1,      0, 0],
					    [ $cos60,      0,-$sin60, 0] ],
		  'Name'     => "S6y^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ $cos60, $sin60,      0, 0],
					    [-$sin60, $cos60,      0, 0],
					    [      0,      0,     -1, 0] ],
		  'Name'     => "S6z^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,      0,      0,  0],
					    [      0,-$cos60, $sin60,  0],
					    [      0,-$sin60,-$cos60,  0] ],
		  'Name'     => "-6x",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$sin60,      0,-$cos60, 0],
					    [      0,     -1,      0, 0],
					    [-$cos60,      0, $sin60, 0] ],
		  'Name'     => "-6y",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$cos60, $sin60,      0, 0],
					    [-$sin60,-$cos60,      0, 0],
					    [      0,      0,     -1, 0] ],
		  'Name'     => "-6z",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [     -1,      0,      0,  0],
					    [      0,-$cos60,-$sin60,  0],
					    [      0, $sin60,-$cos60,  0] ],
		  'Name'     => "-6x^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$sin60,      0,-$cos60, 0],
					    [      0,     -1,      0, 0],
					    [-$cos60,      0, $sin60, 0] ],
		  'Name'     => "-6y^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [-$cos60,-$sin60,      0, 0],
					    [ $sin60,-$cos60,      0, 0],
					    [      0,      0,     -1, 0] ],
		  'Name'     => "-6z^5",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, 0, 1, 0],
					    [ 1, 0, 0, 0],
					    [ 0, 1, 0, 0] ],
		  'Name'     => "3'_111",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, 1, 0, 0],
					    [ 0, 0, 1, 0],
					    [ 1, 0, 0, 0] ],
		  'Name'     => "3'111^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,-1, 0, 0],
					    [ 0, 0, 1, 0],
					    [-1, 0, 0, 0] ],
		  'Name'     => "3'_-111",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, 0,-1, 0],
					    [-1, 0, 0, 0],
					    [ 0, 1, 0, 0] ],
		  'Name'     => "3'_-111^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,-1, 0, 0],
					    [ 0, 0, 1, 0],
					    [-1, 0, 0, 0] ],
		  'Name'     => "3'_1-11",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0, 0, 1, 0],
					    [-1, 0, 0, 0],
					    [ 0,-1, 0, 0] ],
		  'Name'     => "3'_1-11^2",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  1,  0, 0],
					    [ 0,  0, -1, 0],
					    [-1,  0,  0, 0] ],
		  'Name'     => "3'_11-1",
		  'Freedom'  => [0, 0, 0],
		},
		{ 'Matrix' => [ [ 0,  0, -1, 0],
					    [ 1,  0,  0, 0],
					    [ 0, -1,  0, 0] ],
		  'Name'     => "3'_11-1^2",
		  'Freedom'  => [0, 0, 0],
		},
		);

	return @MArrays;
}

sub GetPointGroupGenerators
{
	my @PGArrays = (
		{ 'Name'       => "Oh",
		  'Generators' => ["3'_111", "3'_-111", "3'_1-11", "3'_11-1", '4x', '2x', '2d110'],
		},
		{ 'Name'       => "O",
		  'Generators' => ["3'_111", "3'_-111", "3'_1-11", "3'_11-1", '4x', '2x', '2d110', 'i', 'mx', 'dxy'],
		},
		{ 'Name'       => "Td",
		  'Generators' => ["3'_111", "3'_-111", "3'_1-11", "3'_11-1", 'S4x', 'dxy'],
		},
		{ 'Name'       => "Th",
		  'Generators' => ["3'_111", "3'_-111", "3'_1-11", "3'_11-1", '2x', 'i'],
		},
		{ 'Name'       => "T",
		  'Generators' => ["3'_111", "3'_-111", "3'_1-11", "3'_11-1", '2x'],
		},
		{ 'Name'       => "S6",
		  'Generators' => ['S6z'],
		},
		{ 'Name'       => "S6",
		  'Generators' => ['S6x'],
		},
		{ 'Name'       => "S6",
		  'Generators' => ['S6y'],
		},
		{ 'Name'       => "S4",
		  'Generators' => ['S4z'],
		},
		{ 'Name'       => "S4",
		  'Generators' => ['S4x'],
		},
		{ 'Name'       => "S4",
		  'Generators' => ['S4y'],
		},
		{ 'Name'       => "S3",
		  'Generators' => ['S3z'],
		},
		{ 'Name'       => "S3",
		  'Generators' => ['S3x'],
		},
		{ 'Name'       => "S3",
		  'Generators' => ['S3y'],
		},
		{ 'Name'       => "S2",
		  'Generators' => ['S2z'],
		},
		{ 'Name'       => "S2",
		  'Generators' => ['S2x'],
		},
		{ 'Name'       => "S2",
		  'Generators' => ['S2y'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6z', 'S6z', '2x', 'dxy'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6z', 'S6z', '2y', 'dxy'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6x', 'S6x', '2y', 'dyz'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6x', 'S6x', '2z', 'dyz'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6y', 'S6y', '2z', 'dzx'],
		},
		{ 'Name'       => "D6d",
		  'Generators' => ['6y', 'S6y', '2x', 'dzx'],
		},
		{ 'Name'       => "D4d",
		  'Generators' => ['4z', 'S4z', '2x', '2y', 'dxy'],
		},
		{ 'Name'       => "D4d",
		  'Generators' => ['4x', 'S4x', '2y', '2z', 'dyz'],
		},
		{ 'Name'       => "D4d",
		  'Generators' => ['4y', 'S4y', '2z', '2x', 'dzx'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3z', 'S2z', '2x', 'dxy'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3z', 'S6z', '2x', 'dxy'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3z', 'S6z', '2y', 'dxy'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3x', 'S6x', '2y', 'dyz'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3x', 'S6x', '2z', 'dyz'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3y', 'S6y', '2z', 'dzx'],
		},
		{ 'Name'       => "D3d",
		  'Generators' => ['3y', 'S6y', '2x', 'dzx'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2z', 'S2z', '2x', 'dxy'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2z', 'S2z', '2y', 'dxy'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2x', 'S2x', '2y', 'dyz'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2x', 'S2x', '2z', 'dyz'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2y', 'S2y', '2z', 'dzx'],
		},
		{ 'Name'       => "D2d",
		  'Generators' => ['2y', 'S2y', '2x', 'dzx'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6z', '2x', 'mz'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6z', '2y', 'mz'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6x', '2y', 'mx'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6x', '2z', 'mx'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6y', '2z', 'my'],
		},
		{ 'Name'       => "D6h",
		  'Generators' => ['6y', '2x', 'my'],
		},
		{ 'Name'       => "D4h",
		  'Generators' => ['4z', '2x', '2y', 'mz'],
		},
		{ 'Name'       => "D4h",
		  'Generators' => ['4x', '2y', '2z', 'mx'],
		},
		{ 'Name'       => "D4h",
		  'Generators' => ['4y', '2z', '2x', 'my'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3z', '2x', 'mz'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3z', '2y', 'mz'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3x', '2y', 'mx'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3x', '2z', 'mx'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3y', '2z', 'my'],
		},
		{ 'Name'       => "D3h",
		  'Generators' => ['3y', '2x', 'my'],
		},
		{ 'Name'       => "D2h",
		  'Generators' => ['2z', '2x', '2y', 'mz'],
		},
		{ 'Name'       => "D2h",
		  'Generators' => ['2x', '2y', '2z', 'mx'],
		},
		{ 'Name'       => "D2h",
		  'Generators' => ['2x', '2z', '2x', 'my'],
		},
		{ 'Name'       => "C6h",
		  'Generators' => ['6z', 'mz'],
		},
		{ 'Name'       => "C6h",
		  'Generators' => ['6x', 'mx'],
		},
		{ 'Name'       => "C6h",
		  'Generators' => ['6y', 'my'],
		},
		{ 'Name'       => "C4h",
		  'Generators' => ['4z', 'mz'],
		},
		{ 'Name'       => "C4h",
		  'Generators' => ['4x', 'mx'],
		},
		{ 'Name'       => "C4h",
		  'Generators' => ['4y', 'my'],
		},
		{ 'Name'       => "C3h",
		  'Generators' => ['3z', 'mz'],
		},
		{ 'Name'       => "C3h",
		  'Generators' => ['3x', 'mx'],
		},
		{ 'Name'       => "C3h",
		  'Generators' => ['3y', 'my'],
		},
		{ 'Name'       => "C2h",
		  'Generators' => ['2z', 'mz'],
		},
		{ 'Name'       => "C2h",
		  'Generators' => ['2x', 'mx'],
		},
		{ 'Name'       => "C2h",
		  'Generators' => ['2y', 'my'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6z', 'mx'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6z', 'my'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6x', 'my'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6x', 'mz'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6y', 'mz'],
		},
		{ 'Name'       => "C6v",
		  'Generators' => ['6y', 'mx'],
		},
		{ 'Name'       => "C4v",
		  'Generators' => ['4z', 'mx', 'my'],
		},
		{ 'Name'       => "C4v",
		  'Generators' => ['4x', 'my', 'mz'],
		},
		{ 'Name'       => "C4v",
		  'Generators' => ['4y', 'my', 'mz'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3z', 'mx'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3z', 'my'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3x', 'my'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3x', 'mz'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3y', 'mz'],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ['3y', 'mx'],
		},
		{ 'Name'       => "C2v",
		  'Generators' => ['2z', 'mx'],
		},
		{ 'Name'       => "C2v",
		  'Generators' => ['2z', 'my'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6z', '2x'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6z', '2y'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6x', '2y'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6x', '2z'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6y', '2z'],
		},
		{ 'Name'       => "D6",
		  'Generators' => ['6y', '2x'],
		},
		{ 'Name'       => "D4",
		  'Generators' => ['4z', '2x', '2y'],
		},
		{ 'Name'       => "D4",
		  'Generators' => ['4x', '2y', '2z'],
		},
		{ 'Name'       => "D4",
		  'Generators' => ['4y', '2y', '2z'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3z', '2x'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3z', 'C2y'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3x', '2y'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3x', '2z'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3y', '2z'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ['3y', '2x'],
		},
		{ 'Name'       => "D2",
		  'Generators' => ['2z', '2x', '2y'],
		},
		{ 'Name'       => "C6",
		  'Generators' => ['6x'],
		},
		{ 'Name'       => "C6",
		  'Generators' => ['6y'],
		},
		{ 'Name'       => "C6",
		  'Generators' => ['6z'],
		},
		{ 'Name'       => "C4",
		  'Generators' => ['4x'],
		},
		{ 'Name'       => "C4",
		  'Generators' => ['4y'],
		},
		{ 'Name'       => "C4",
		  'Generators' => ['4z'],
		},
		{ 'Name'       => "C3",
		  'Generators' => ['3x'],
		},
		{ 'Name'       => "C3",
		  'Generators' => ['3y'],
		},
		{ 'Name'       => "C3",
		  'Generators' => ['3z'],
		},
		{ 'Name'       => "D3",
		  'Generators' => ["3'_111", "dxy", "2d-101"],
		},
		{ 'Name'       => "D3",
		  'Generators' => ["3'_-111", "dxy", "2d-101"],
		},
		{ 'Name'       => "D3",
		  'Generators' => ["3'_1-11", "dxy", "2d-101"],
		},
		{ 'Name'       => "D3",
		  'Generators' => ["3'_11-1", "dxy", "2d-101"],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ["3'_111", "dxy"],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ["3'_-111", "dxy"],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ["3'_1-11", "dxy"],
		},
		{ 'Name'       => "C3v",
		  'Generators' => ["3'_11-1", "dxy"],
		},
		{ 'Name'       => "C3",
		  'Generators' => ["3'_111"],
		},
		{ 'Name'       => "C3",
		  'Generators' => ["3'_-111"],
		},
		{ 'Name'       => "C3",
		  'Generators' => ["3'_1-11"],
		},
		{ 'Name'       => "C3",
		  'Generators' => ["3'_11-1"],
		},
		{ 'Name'       => "C2",
		  'Generators' => ['2x'],
		},
		{ 'Name'       => "C2",
		  'Generators' => ['2y'],
		},
		{ 'Name'       => "C2",
		  'Generators' => ['2z'],
		},
		{ 'Name'       => "Ci",
		  'Generators' => ['i'],
		},
		);

	return @PGArrays;
}

1;