/* www-ATLAS of Group Representations. L3(4):2a represented as 90 x 90 matrices over GF(3). */ F:=GF(3); x:=CambridgeMatrix(1,F,90,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000020000010000000200000000100000200000000000000000000000000000", "000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", "000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000", "022010122002210021100102201100201021122200210122211111210112122110200121221120100022212201", "000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000", "022101112021120001120210022020221221220112221110111220012212102121210101210222210121121122", "000000000000000000000000000000010000010000000200000000200000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000", "001112111102111110011121210021212202121000011121211201121020112121202001201020222201022022", "011112110201110210002121001212201020210111200220220221220002101110100111111220121112111101", "000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000", "102002011002000201221122120202012021221121211100002110200100001000221020120121110101222100", "000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000", "220011112201121010110012011112201011220122100102200122221012111200120202102122212011011121", "000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000", "201101112121120000102002111020021110220220100002122000220210111022210222010220020102222100", "000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000", "110200022220102112210021100021202211212102011121100110022222202010102220001012211110012122", "200212221102200022110221200112112201202010222210100200001011122111212122021220222201212012", "000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000", "001120021020211200020202201022112010202102112222122000010221102122202020210122002111200020", "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000", "001212000100010000000000000000200000100000020000000010000000000000000000000000000000000200", "002021120101022021020020121002210220120111111110002021220220012012212112022200202002020202", "000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000"]); y:=CambridgeMatrix(1,F,90,[ "001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "211200000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "222200000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000", "010012000000000000000200010000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000", "122000000000001000000000000000000000001000000002000000000000000000000000000000000000000000", "100022000000000000000100010000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000", "220200000000000001000000000000000000002000000002000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000", "000012010220100110010000220201111011022022010022120000122001020210212211220121201122000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010", "012101110020201000110021121221012012120210001001000211020022021221111122000010110101211210", "102100220112102020020101102121201210200212000111121020001011100100122012222200110101211011", "101221020001011200200221100110011001101011020021222100020202110011210120200020210001002202", "000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000", "002102200012202122001012222121202022210122020021012120220212000002110222111200111121211011", "101021100221102100011221211121212122221020012212221221002022120212221110102222200220020012", "200221221221022110010022120112210200212120022021020212021210102222201201212221212212121002", "222111102222000210201222111112010022120020220122012120210211222020101212211220002112222220", "000200120211021121011112102122110121102221120111022011100210201122222211120212120000021202", "020121102222011112112010121022020102121221001110101212112000002210201110202201001020001100", "010020012221121122112022100120011211111010112220222020122002221211211120021220220100020002", "210112202221100002221121011102222210222201022211200120110100112211021021120110010011222101", "112212100210101111121111201221000100011122122111002111200022101010100200020012121102112001", "220111222101110202101011100211010012222222102200111001201000212212100110112120111101122011", "020121102220101221111110012221211111211002002100222210121000212202110211220011012000220212", "121212210022002210010220021101222220110020202102210012102121212011210201120201021221211200", "212100220000110221002021220112001112201000020121222122000112211210101210121100121220021022", "000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000", "200101111110100002022102122021102220002200111121011201222022222001101212202120011110122200", "002010200122002102022010002011020102210201221220101210212021001200022210112101220201220111", "000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000", "221110011101211010001112112111020111221100021022112110212120201001120210022210102100210011", "001211011110202102122110202012002112112101112020002102200221110022112020110102220221110002", "010122200212102210122120101111001101011211111212100201202021120221111022212211101110212101", "210122022122122122002110012202011102111221121111200010112002021211122011110102121011112200"]); G:=MatrixGroup<90,F|x,y>; print "Group G is L3(4):2a < GL(90,GF(3))";