
print "The unitary group U( 3, 5 ) represented as a";
print "permutation group of degree 525. ";
print "Order: 126,000 = 2^4 * 3^2 * 5^3 * 7;  Base: 1,2,3. ";
print "Group: G";

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