/* www-ATLAS of Group Representations. J1 represented as 76 x 76 matrices over GF(3). */ F:=GF(3); x:=CambridgeMatrix(1,F,76,[ "0100000000000000000000000000000000000000000000000000000000000000000000000000", "1000000000000000000000000000000000000000000000000000000000000000000000000000", "0000100000000000000000000000000000000000000000000000000000000000000000000000", "0000010000000000000000000000000000000000000000000000000000000000000000000000", "0010000000000000000000000000000000000000000000000000000000000000000000000000", "0001000000000000000000000000000000000000000000000000000000000000000000000000", "0000000010000000000000000000000000000000000000000000000000000000000000000000", "0000000001000000000000000000000000000000000000000000000000000000000000000000", "0000001000000000000000000000000000000000000000000000000000000000000000000000", "0000000100000000000000000000000000000000000000000000000000000000000000000000", "0000000000000100000000000000000000000000000000000000000000000000000000000000", 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"1212210121202101221202100220022202201222210210020001120000010101000000021100", "0000000000000000000000000000000000000000000000000000000000010000000000000000", "0000000000000000000000000000000000000000000000000000000000000100000000000000", "0000000000000000000000000000000000000000000000000000000000000000010000000000", "1101002021200020211122221212212111202220012021002200110021222021020220221012"]); y:=CambridgeMatrix(1,F,76,[ "0010000000000000000000000000000000000000000000000000000000000000000000000000", "0001000000000000000000000000000000000000000000000000000000000000000000000000", "0112000000000000000000000000000000000000000000000000000000000000000000000000", "2110000000000000000000000000000000000000000000000000000000000000000000000000", "0000001000000000000000000000000000000000000000000000000000000000000000000000", "0000000100000000000000000000000000000000000000000000000000000000000000000000", "0110202000000000000000000000000000000000000000000000000000000000000000000000", 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"0000000000000000000000000000000000000000000010000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000000000000000001", "0012221022100102201001111100112100212010121122111210201000012020121021210212", "2202021120012200202010201211200121011221102212211211111212200012111102122212", "2220201001121112012122201121001012122110020000211101220112012002011201011221", "2200022220220121202120211101020122111221022222002200112212122020200111020222", "2112102002110022201212111101211220121211220121122012001122201201220102122121", "1220100212002022022001000110122222022111220112020201212002122121000212020201", "0000000000000000000000000000000000000000000000000000000100000000000000000000"]); G:=MatrixGroup<76,F|x,y>; print "Group G is J1 < GL(76,GF(3))";