/* 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", "000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000002000000000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000", "000000102000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000001", "022121210012001022121012121001112000122211222012201011111111201012102001211", "122020010220101120010012012102022211112121002000221011220201011011221002120", "000000000000000000000000000000000000000000000000100000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000", "021011211121210111002000111010212101010110100222112012101022220110020020210", "000000000000000000000000000000000000000000000000001000000000000000000000000", "222201011222022200012202020001220200012122122101022220101120000210211000000", "020200201022211012011110221020210101010010100122022212101202211210220020211", "000000000000000000000000000000000000000000000000000010000000000000000000000", "122001121021102220121110022012202002211201212211100110200121102001220000122", "121221020112020210201210212100211112221211021012222210021201112212112202121", "000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000", "110010201211011202002221020210020220100221221100112110122110010102122022200", "000002101212112010120102110002201001122100101210221002122200021122112022022", "000000000000000000000000000000000000000000000000000000000010000000000000000"]); y:=CambridgeMatrix(1,F,75,[ "210000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000", "221000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000", 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"000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000010", "210122022120010222002000100200122221220000012012112002202002200201000102200", "000000000000000000000000000000000010000000000000000000000000000000000000000", "222212020010202000020021021221011121221212001002112022110102022022112001210", "012211110010102210120001220111112021211221100200000221100111122010102220211", "122112000211202122221121200122220210021101022212211222222212202222102020111", "022021121221211102010012211210100020200112002001221101010210111222210202101", "000000000000000000000000000000000000010000000000000000000000000000000000000", "102020212121221121110120112202212022220001001100222201110020221022022102121", "000000000000000000000000000000000000001000000000000000000000000000000000000", "221211121202221110100001120121121220121002221122120012020021021010021002121", "021111212120022011211021200022202011121201000122201000222012202200200002101", "000000000000000000000000000000000000000010000000000000000000000000000000000", "210111102202100220001001200011021021012002002102120200100220210102111212210", "020021012001222102022110000021020000212012111110210010202112220200102002120", "211012202001012112201010201220121110221002001012002021121120120202001222210", "000000000000000000000000000000000000000000010000000000000000000000000000000", "201221012100000211102220211212102212110200001220110201220122110010222100111", "202110022122022021112120121200012222202100211200211220002122110201210112201"]); G:=MatrixGroup<75,F|x,y>; print "Group G is U3(4) < GL(75,GF(3))";