/*
www-ATLAS of Group Representations.
2.PGL2(7) represented as permutations on 672 points.
*/

G<x,y>:=PermutationGroup<672|\[
2,6,9,1,13,4,17,19,15,3,18,20,16,5,10,14,11,7,12,8,37,39,38,40,41,
43,42,44,45,47,46,48,49,51,50,52,23,21,24,22,27,25,28,26,31,29,32,30,35,33,
36,34,85,87,86,88,89,91,90,92,93,95,94,96,97,99,98,100,101,103,102,104,105,107,106,
108,109,111,110,112,113,115,114,116,55,53,56,54,59,57,60,58,63,61,64,62,67,65,68,66,
71,69,72,70,75,73,76,74,79,77,80,78,83,81,84,82,180,181,178,182,183,185,184,186,187,
160,188,158,189,191,190,192,193,195,194,196,171,197,169,198,199,201,200,202,203,151,204,149,146,205,
148,206,207,209,208,210,211,126,212,128,213,215,214,216,217,219,218,220,137,221,139,222,223,225,224,
226,227,117,228,119,120,118,123,121,124,122,127,125,131,129,132,130,135,133,136,134,140,138,143,141,
144,142,147,145,152,150,155,153,156,154,159,157,163,161,164,162,167,165,168,166,172,170,175,173,176,
174,179,177,301,303,302,304,305,306,307,309,308,310,311,313,312,314,315,317,316,318,319,320,321,323,
322,324,325,327,326,328,329,331,330,332,333,335,334,336,337,339,338,340,341,342,343,345,344,346,347,
349,348,350,351,353,352,354,355,356,357,359,358,360,361,363,362,364,365,367,366,368,369,371,370,372,
231,229,232,230,234,233,237,235,238,236,241,239,242,240,245,243,246,244,248,247,251,249,252,250,255,
253,256,254,259,257,260,258,263,261,264,262,267,265,268,266,270,269,273,271,274,272,277,275,278,276,
281,279,282,280,284,283,287,285,288,286,291,289,292,290,295,293,296,294,299,297,300,298,469,470,461,
471,463,472,473,475,474,476,477,466,478,468,479,480,481,441,482,443,438,483,440,484,485,487,486,488,
489,490,491,455,492,457,452,493,454,494,495,496,423,497,425,498,499,432,500,434,501,502,415,503,413,
504,505,507,506,508,509,420,510,418,511,512,513,395,514,393,392,515,390,516,517,519,518,520,521,522,
523,409,524,407,406,525,404,526,527,528,377,529,375,530,531,386,532,384,374,373,378,376,381,379,382,
380,385,383,388,387,391,389,396,394,399,397,400,398,402,401,405,403,410,408,412,411,416,414,419,417,
422,421,426,424,429,427,430,428,433,431,436,435,439,437,444,442,447,445,448,446,450,449,453,451,458,
456,460,459,464,462,467,465,584,589,582,590,591,592,593,594,577,578,571,595,573,596,597,598,569,570,
599,600,601,563,602,561,603,586,604,588,554,605,556,606,607,608,609,610,550,549,545,611,543,612,613,
614,542,541,615,616,617,533,618,535,619,560,620,558,536,534,538,537,540,539,546,544,548,547,552,551,
555,553,559,557,564,562,566,565,568,567,574,572,576,575,580,579,583,581,587,585,637,638,639,640,641,
642,643,644,645,646,647,648,649,650,651,652,622,621,624,623,626,625,628,627,630,629,632,631,634,633,
636,635,661,662,663,664,665,666,667,668,654,653,656,655,658,657,660,659,672,671,669,670]
,\[
3,7,5,11,1,15,8,2,21,23,12,4,25,27,16,6,29,31,33,35,22,9,24,10,26,
13,28,14,30,17,32,18,34,19,36,20,53,55,57,59,61,63,65,67,69,71,73,75,77,79,
81,83,54,37,56,38,58,39,60,40,62,41,64,42,66,43,68,44,70,45,72,46,74,47,76,
48,78,49,80,50,82,51,84,52,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,147,
149,151,153,155,157,159,161,163,165,167,169,171,173,175,177,179,118,85,120,86,122,87,124,88,126,
89,128,90,130,91,132,92,134,93,136,94,138,95,140,96,142,97,144,98,146,99,148,100,150,101,
152,102,154,103,156,104,158,105,160,106,162,107,164,108,166,109,168,110,170,111,172,112,174,113,176,
114,178,115,180,116,229,231,233,234,235,237,239,241,243,245,247,248,192,191,249,251,253,255,257,259,
184,183,261,263,265,267,269,270,271,273,275,277,279,281,283,284,216,215,285,287,289,291,293,295,208,
207,297,299,230,181,232,182,202,201,236,185,238,186,240,187,242,188,244,189,246,190,194,193,250,195,
252,196,254,197,256,198,258,199,260,200,262,203,264,204,266,205,268,206,226,225,272,209,274,210,276,
211,278,212,280,213,282,214,218,217,286,219,288,220,290,221,292,222,294,223,296,224,298,227,300,228,
373,374,375,377,379,381,383,385,387,388,310,309,389,391,393,395,302,301,397,399,401,402,403,405,407,
409,411,412,328,327,413,415,417,419,322,321,421,422,423,425,427,429,431,433,435,436,346,345,437,439,
441,443,338,337,445,447,449,450,451,453,455,457,459,460,364,363,461,463,465,467,358,357,318,317,376,
303,378,304,380,305,382,306,384,307,386,308,312,311,390,313,392,314,394,315,396,316,398,319,400,320,
336,335,404,323,406,324,408,325,410,326,330,329,414,331,416,332,418,333,420,334,354,353,424,339,426,
340,428,341,430,342,432,343,434,344,348,347,438,349,440,350,442,351,444,352,446,355,448,356,372,371,
452,359,454,360,456,361,458,362,366,365,462,367,464,368,466,369,468,370,533,535,537,538,472,471,539,
540,497,498,543,545,547,548,491,492,551,552,482,481,553,555,549,550,485,486,557,559,541,542,475,476,
561,563,565,566,504,503,567,568,529,530,571,573,575,576,523,524,579,580,514,513,581,583,577,578,517,
518,585,587,569,570,507,508,534,469,536,470,474,473,499,500,477,478,544,479,546,480,488,487,483,484,
493,494,554,489,556,490,558,495,560,496,562,501,564,502,506,505,531,532,509,510,572,511,574,512,520,
519,515,516,525,526,582,521,584,522,586,527,588,528,621,622,603,604,625,626,594,593,627,628,589,590,
598,597,623,624,629,630,619,620,633,634,610,609,635,636,605,606,614,613,631,632,599,600,591,592,596,
595,602,601,615,616,607,608,612,611,618,617,653,654,638,637,655,656,642,641,657,658,646,645,659,660,
650,649,640,639,644,643,648,647,652,651,669,670,662,661,671,672,666,665,664,663,668,667]
>;
print "Group G is 2.PGL2(7) < Sym(672)";