/* www-ATLAS of Group Representations. U3(4) represented as 75 x 75 matrices over GF(3). */ F:=GF(3); x:=CambridgeMatrix(1,F,75,[ "010000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000", "212121000001002000100000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000", "021010000002000000200000000000000000000000200000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000010", "110101210122022001002011020002111221201021000011012210022001022110012100010", "000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000", "110101122202102211021110221122021012102102002102220221121010111110022110210", "000000000000000000000000000000000000000000000000100000000000000000000000000", "102011022010220010212000112212020021210210120120022202222000002110001221221", "211010020201102211202011001012100102120001020202200001021100202020000000110", "001202102222110022011021120112120200002201222020202012220201000122212122002", "000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000", "212201200212001010201001022102120101200002222102110120220102202120021122022", "201001001111122102111122121010202020011010122102201100101221012100102011001", "000000000000000000000000000000000000000000000000000000100000000000000000000", "020110002211100022220221200012100101212021220020002201212011220200201221022", "000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000", "200202220222221022102022022020211100110220011221001212200112022110012120122"]); y:=CambridgeMatrix(1,F,75,[ "001000000000000000000000000000000000000000000000000000000000000000000000000", "022000000000000000000000000000000000000000000000000000000000000000000000000", "121000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000", 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"000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "201202120211011102001022010001222102102012000022021120011002011220021200020", "000000000000000000000000000000000000000000000000000000000000000000000000001", "110010000000110121101202120001000110020102212211200121120211021101101020201", "212222020000122001201010201100202100200202212012010001012020101211102111212", "000000000000000000000000000000000000100000000000000000000000000000000000000", "001221112122010121111012001222220021211200102102102122001022220112002220101", "000000000000000000000000000000000000010000000000000000000000000000000000000", "101111020212012001101222120001221220020220021011212000220200012022111101010", "222211211211202220102010222120000002121201222212020001112100020010101201010", "210002221220122211011101020212220021011020110112211021101220220201120221202", "220001200111020112022120202220002021001201110221110110210101021101220102120", "000000000000000000000000000000000000000010000000000000000000000000000000000", "202002021010121012010102011201210102022201200222212100101121121110222210012", "011010021202012010201112222100212111201110101222120200201011212101221120000", "010211022010112201220220010221002200020011001001201021220120120211020102022", "200011022202002121002211221112101112102210220012002011210120110120102112001", "121221222012001011020022112001220001002021101121001101010022101102010121121", "000000000000000000000000000000000000000000000100000000000000000000000000000"]); G:=MatrixGroup<75,F|x,y>; print "Group G is U3(4) < GL(75,GF(3))";