
print "The unitary group U( 4, 3 ) represented as a";
print "permutation group of degree 540. ";
print "Order: 3,265,920 = 2^7 * 3^6 * 5 * 7;  Base: 1,2,3. ";
print "Group: G";

G := PermutationGroup< 540  |
    \[     2,    4,    6,    7,    9,   10,   12,   14,   15,
   17,   19,   20,   22,   23,   25,   27,   28,   30,   31,   33,
   35,   36,   38,   39,   40,   42,   43,   45,   46,   47,   26,
   50,    1,   52,   53,   55,   57,   58,   59,   61,   63,   64,
   66,   68,   69,   71,   73,   75,   76,   77,   78,   79,   81,
   83,   84,   86,   87,   89,   91,   92,   93,   95,   96,   98,
  100,  101,  103,  104,    3,   24,  106,   18,  108,  110,  111,
  113,  115,  116,  118,  120,  121,  123,  124,  126,  128,  129,
  130,  132,  133,  135,  136,  138,    5,  141,  142,  144,  146,
   11,  148,  149,  150,  152,  153,  155,  157,  158,  160,  161,
  163,  164,  166,  168,  169,  171,  172,  174,  175,  176,  178,
  179,  180,  182,  183,   51,  184,  185,  187,  188,  190,  191,
  192,  193,    8,  196,  197,  199,  201,  202,  139,  204,  205,
  207,  209,  210,  212,  213,  215,   65,  216,  217,  218,  219,
  221,   44,  223,  225,  226,  228,  230,  231,   72,  233,  203,
  235,  237,  238,  239,  165,  241,  243,  244,  246,  159,   54,
  248,  250,  252,  253,  255,  257,  259,  260,  137,  224,   13,
  265,  208,  267,  269,  270,  272,  273,  275,  277,  274,  278,
  279,  281,   70,  282,  242,  284,  286,  112,  288,  289,  290,
  292,  293,  211,  295,  206,  296,  298,  125,  299,   16,  302,
  304,  291,  306,   49,  308,  310,  311,   97,   60,  313,  315,
  316,  317,  319,  320,  307,  170,  323,  324,  326,  181,  329,
  330,  332,  333,  335,  337,  338,  340,  287,  341,  342,  276,
  344,  346,  189,  348,  318,   21,  350,  266,  145,  114,  353,
  354,  355,  356,  358,  359,  360,  361,  363,  365,  366,  367,
   88,  369,  371,  372,  322,  375,  377,  263,  379,  151,  381,
  234,  383,  384,  382,  122,  385,  386,  387,  327,   67,   41,
  105,  390,  297,   99,  391,  256,  328,  102,  393,  394,  395,
  321,  154,  396,  397,  398,  399,   29,  401,  402,  404,  405,
  407,  408,  409,  410,  264,  411,  140,  413,  414,  415,  416,
  194,  222,  419,   82,   74,  314,  421,  422,  423,   32,  426,
  200,  428,   34,  312,  131,  430,  431,  336,  433,  435,  240,
  436,  437,  438,  439,  440,  441,  392,  443,  444,  445,  268,
  447,  448,  450,  451,   37,  177,  347,  195,  454,  156,  258,
  455,  373,  456,  285,  173,  376,  458,  460,  227,  461,  462,
  463,  464,  465,  345,  467,  468,  449,  470,  471,  424,  162,
  294,  472,  147,  251,  475,  420,  476,  469,   90,  280,  479,
  220,  481,  482,  484,  378,  331,  418,  480,   48,  488,  490,
  491,  352,  349,  249,  492,  325,  493,  303,  143,  232,   85,
  494,  214,  127,  495,  370,  496,  497,  236,  498,  474,  500,
  502,  134,  309,  351,  167,  427,  254,  506,  507,   56,  499,
  508,  483,  509,  504,  229,  503,  403,  400,  489,  510,  511,
  512,  473,  513,   62,  417,  515,  516,  380,  432,  374,  517,
  186,  109,  487,  514,  518,  434,  519,  520,  368,  453,  522,
  524,  305,  526,  334,  527,  425,  247,  283,  406,  261,  529,
  457,  528,   80,  452,  362,  429,  459,  262,  531,  300,  301,
  532,  271,  442,  505,  533,  501,  525,   94,  117,  485,  523,
  534,  466,  521,  364,  107,  486,  339,  357,  446,  537,  343,
  412,  119,  538,  477,  198,  478,  530,  539,  388,  535,  389,
  540,  536,  245 ],
    \[     3,    5,    1,    8,    2,   11,   13,    4,   16,
   18,    6,   21,    7,   24,   26,    9,   29,   10,   32,   34,
   12,   37,   28,   14,   41,   15,   44,   23,   17,   48,   49,
   19,   51,   20,   54,   56,   22,   38,   60,   62,   25,   65,
   67,   27,   70,   72,   74,   30,   31,   59,   33,   80,   82,
   35,   85,   36,   88,   90,   50,   39,   94,   40,   97,   99,
   42,  102,   43,  105,   77,   45,  107,   46,  109,   47,  112,
  114,   69,  117,  119,   52,  122,   53,  125,  127,   55,  120,
  131,   57,  134,   58,  137,  139,  140,   61,  143,  145,   63,
  147,   64,  116,  151,   66,  154,  156,   68,  159,   71,  162,
   73,  165,  167,   75,  170,   76,  173,  100,   78,  177,   79,
   86,  181,   81,  174,  150,   83,  186,   84,  189,  130,  129,
   87,  194,  195,   89,  198,  200,   91,  203,   92,   93,  206,
  208,   95,  211,   96,  214,   98,  148,  210,  124,  101,  220,
  222,  103,  224,  104,  227,  229,  106,  166,  232,  108,  234,
  236,  110,  160,  111,  240,  242,  113,  245,  247,  115,  123,
  249,  251,  118,  254,  256,  258,  121,  261,  262,  263,  264,
  126,  266,  268,  128,  271,  212,  274,  276,  132,  133,  199,
  280,  135,  196,  136,  283,  285,  138,  287,  205,  141,  291,
  142,  294,  149,  144,  191,  297,  146,  299,  300,  301,  303,
  305,  152,  307,  153,  309,  155,  296,  312,  157,  314,  158,
  298,  318,  161,  321,  163,  322,  164,  325,  327,  328,  168,
  331,  169,  334,  336,  171,  339,  172,  335,  175,  343,  176,
  345,  347,  178,  349,  179,  288,  180,  351,  352,  182,  183,
  184,  185,  357,  187,  311,  188,  362,  364,  190,  341,  368,
  192,  370,  193,  373,  374,  376,  197,  378,  380,  201,  382,
  202,  324,  204,  257,  365,  295,  207,  388,  389,  209,  290,
  225,  213,  230,  215,  216,  217,  392,  218,  381,  219,  306,
  221,  316,  223,  333,  267,  226,  400,  228,  403,  308,  406,
  231,  342,  350,  233,  235,  412,  286,  237,  326,  238,  239,
  417,  418,  241,  420,  310,  243,  248,  244,  424,  425,  246,
  427,  272,  319,  250,  429,  252,  432,  253,  434,  255,  320,
  259,  260,  355,  435,  353,  442,  265,  393,  428,  446,  372,
  269,  449,  270,  289,  394,  452,  273,  453,  275,  395,  361,
  277,  278,  457,  279,  423,  281,  459,  282,  304,  284,  422,
  407,  385,  451,  466,  292,  293,  469,  421,  302,  358,  366,
  371,  473,  474,  444,  419,  313,  463,  477,  315,  478,  480,
  317,  384,  483,  430,  410,  485,  323,  486,  487,  489,  445,
  329,  330,  399,  332,  391,  383,  377,  337,  338,  426,  340,
  359,  344,  409,  431,  346,  448,  348,  354,  499,  491,  501,
  503,  504,  505,  356,  450,  398,  416,  360,  456,  433,  363,
  443,  386,  367,  369,  462,  481,  447,  375,  475,  379,  472,
  494,  454,  401,  514,  500,  387,  509,  510,  390,  470,  488,
  460,  396,  397,  458,  506,  402,  404,  521,  405,  455,  523,
  408,  525,  411,  413,  414,  471,  415,  528,  437,  516,  530,
  461,  517,  531,  511,  508,  436,  465,  438,  518,  439,  440,
  441,  476,  532,  498,  467,  468,  497,  520,  534,  464,  535,
  492,  495,  502,  519,  512,  479,  536,  482,  537,  484,  527,
  526,  490,  529,  493,  496,  507,  538,  513,  515,  522,  524,
  533,  540,  539 ]>;
AssertAttribute(G, "Order", 2^7 * 3^6 * 5 * 7);
