/*
www-ATLAS of Group Representations.
4b.L3(4) represented as permutations on 480 points.
*/

G<x,y>:=PermutationGroup<480|\[
1,6,3,12,5,2,18,15,17,10,23,4,26,27,8,33,9,7,36,38,31,40,11,43,46,
13,14,52,49,51,21,45,16,41,57,19,63,20,61,22,34,67,24,69,32,25,73,74,29,80,
30,28,83,85,78,86,35,91,88,90,39,96,37,99,100,101,42,104,44,107,108,111,47,48,116,
113,115,55,121,50,124,125,53,130,54,56,95,59,136,60,58,139,140,98,87,62,143,94,64,65,
66,150,152,68,155,158,70,71,163,162,72,166,76,169,77,75,172,174,167,176,79,179,182,81,82,
156,185,187,190,84,193,194,196,197,198,89,201,202,92,93,205,206,97,210,209,211,213,214,216,102,
219,103,221,223,105,126,226,106,230,231,234,110,109,238,239,112,119,192,114,243,244,117,204,118,248,
120,200,183,122,254,253,123,178,257,127,186,128,215,227,129,265,168,131,132,222,133,134,135,276,177,
137,138,236,173,141,142,235,283,145,144,146,245,147,148,188,149,233,272,151,268,153,195,154,240,297,
157,189,228,301,159,160,304,217,161,207,203,307,164,165,224,264,309,170,171,212,312,314,175,279,275,
315,316,181,180,320,321,184,325,322,324,261,262,328,241,191,333,332,220,335,270,337,218,339,340,250,
199,281,342,249,343,277,286,208,344,345,282,296,346,289,348,349,319,293,351,352,287,225,323,355,300,
229,331,357,232,359,341,237,362,242,365,366,246,371,247,251,252,338,374,292,255,256,259,298,260,258,
377,378,263,380,381,302,267,266,384,269,385,271,317,273,274,306,278,280,284,285,288,386,290,291,387,
294,295,391,392,299,394,303,395,305,396,398,308,401,404,310,311,367,406,408,411,313,414,415,318,417,
418,326,327,416,329,330,423,425,334,336,347,350,431,432,434,353,354,424,356,358,360,397,361,440,442,
363,436,443,364,446,368,438,369,409,410,370,439,433,372,373,379,375,376,441,453,454,437,382,393,383,
452,458,444,455,457,388,389,413,390,460,402,422,407,412,399,419,400,403,428,463,405,448,447,451,465,
449,426,420,421,429,467,430,427,468,435,469,470,445,472,450,474,456,459,461,462,473,464,471,466,476,
475,478,477,480,479]
,\[
2,7,8,1,9,14,4,19,20,21,3,24,5,28,29,6,30,35,11,13,39,10,41,44,12,
45,48,16,53,54,55,15,56,17,58,59,18,60,22,33,66,23,31,25,70,71,26,75,76,27,
77,82,32,34,68,65,87,37,92,93,94,36,97,38,40,42,102,43,105,47,109,46,110,111,50,
117,118,119,49,122,51,126,127,52,128,132,134,99,57,96,138,62,64,141,61,142,144,63,145,146,
148,151,67,153,156,69,157,160,72,164,165,73,152,74,166,171,79,81,175,78,177,180,80,181,184,
84,188,189,83,191,85,195,86,89,88,199,90,91,203,204,95,137,207,98,135,212,100,215,101,217,
103,220,222,104,224,106,227,228,107,232,108,233,236,112,114,240,213,113,193,115,245,246,116,247,120,
250,251,121,201,123,255,176,124,258,259,125,260,129,131,263,266,130,267,268,133,270,272,274,277,136,
278,172,139,140,279,234,281,143,282,285,231,147,287,239,149,289,291,150,249,168,292,154,294,295,155,
296,159,299,158,300,303,161,305,306,162,248,163,202,308,170,167,169,223,311,173,238,219,237,174,256,
178,179,210,318,183,182,321,186,326,327,185,187,329,190,330,192,242,334,194,336,196,338,197,341,198,
342,200,252,205,206,208,316,344,209,317,211,241,214,347,216,218,350,221,310,225,353,322,226,229,356,
328,230,286,337,235,280,360,288,363,243,367,368,244,369,373,284,253,346,254,354,375,320,257,315,376,
261,262,379,264,349,265,358,382,269,324,271,332,273,343,276,275,345,283,339,340,319,290,351,331,293,
388,389,298,297,325,302,301,304,348,397,307,399,402,309,403,404,313,409,410,312,412,314,335,416,323,
393,419,420,357,421,392,424,333,426,387,377,430,359,418,352,433,381,355,378,417,437,361,439,441,362,
443,364,444,445,365,425,366,446,370,372,449,450,371,451,431,374,395,390,429,436,455,380,401,383,456,
457,384,385,386,428,415,411,453,460,391,394,461,396,462,398,400,434,454,405,407,464,406,408,459,413,
466,414,435,423,422,447,427,442,432,458,438,440,471,448,463,452,475,467,477,469,473,479,465,472,476,
468,478,470,480,474]
>;
print "Group G is 4b.L3(4) < Sym(480)";