/* www-ATLAS of Group Representations. E6(4) represented as 78 x 78 matrices over GF(4). */ F:=GF(4); x:=CambridgeMatrix(1,F,78,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000000", "000000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000000000000000000000000000000000000010", "223103121210213201302032221131332310120303313020312312203213300202323020231033", "133301001213302331332201123233132331103021231012003230111232132321122000211203", "123313210303200230222101203120313333310123032232200310232332100211102121002212", "302232132330303312230002203122223301303012220300303002110120022132233311012210", "213001211133312232230001220011123330113013100133000100002012331121303322230003", "110133312311000133110101223202203230010121100230331030300310311022302211200131", "313211303301321331122201310101020120003020231202011021132101330002220302133021", "210133222202131230011323032123211103302320030210132102321331000231032131303113", "322103122331331021210223221120321022112212310203122232231302300233002233012031", "331201031032233123011011202132322111332200003300333030332310121012123302132133", "113132313220110011210023112122111131301331202003230000121231001133233100123130", "230320311232022322223013211111033103130222122121121000210123013123002010101230", "020123130300210013220222023302322222103022131110032332210331321030013311101002", "212011131023010303301103112102022310333320013012233100102321213101102110123100", "120211321103111121230313121011130131023030232012013323330102320011120111133021", "223301020220022333202211223003311021121201031301230203320121102031201221111100", "032322331110301102110031323001201212120101131000120310202021210321021233232220", "330120213123002132013213033011023332303101332010312220100130302101110011021322", "103033123211001112110231213210201222122333103300002103102210230233223022233230", "130103313312010312112100031330222222310213112103013113133332233321302320032212", "222320032221122330113112230113212322100331221212322313230321003132322133232100", "203123101013321330320002102203113101000221032010021101231312210113122020132113", "112010221023012031223320112011231121301301311200312232131321113203012022301231", "220010231101000020111130111201221013013001000233320131002313113322113030022232", "021033322133330202223111332110011311231012123300111332022203123222203123120033", "013312020103321103121012310101230121022033113120000322311133102133011020021032", "111301011033323311300210010222202102030123132231203111131103031121122001202300", "120020213212313213021312011003311300003233202000120001120310233011230213031120", "110320300231133011221232210102212031333312100112103110011000212301310332331302", "020122030321131013303032100303130012103033201200020022212231313302222102010310", "110313010202233200031202322031010112300331020011300230003213013003223102200030", "112021222032130220332320323003212320202220201010132201310032202023101033300222", "332202320230101130132203313320000211331333002330100210322030113110033100201300", "100300231010001231132302222122223223223020130322032221210200303032322312102130", "231021213021121333313121323030113120212011230032002331003321102323301130223233", "300231221213312222300310220203302131331301132303212000122020031113301030301213", "323201210031231201312020101030301130222222310131131221023023231232300220332211", "023302300211313110223201213323110222322032302033200002231231222322232110203101", "232222113311212221200111021011322203231023300022322120122000312021131001011001"]); y:=CambridgeMatrix(1,F,78,[ "001000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000", "010001100000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000000001", "033333010212013211013112322121121300323310111112102303202211211203213322133321", "003032333313021203331022111102312300211013330320003300213322122012131120312013", "033030303313002120102121121130222311100213032120100211122002202000232331330030", "201012000132233311331122303133231203112021201003123032112030030330123212120323", "013032110331311202221023102100222132321101231330001022322003303332033021322220", "323301210212120000102200113231322222131212132111203023313000010233213332131100", "010323031203211011320020202010012030300112220212010301020111302003003303213301", "221313211231101222110222001333002321003111101120013330031001300132010031011030", "022212030201021023101303311233003302223132123103221012003003031031211303132132", "111322033202002132130131222013333121011323233213332323202322200003223301310322", "211303111301032113322131200021031332203331232322021032112003022001001232333032", "121111311320120010301203111111011313220021023211330210203113331131101203221223", "322011033110132101310100300203232201312103311102330133001322321333233002333022", "320221103320131011330321231130212000231020203131323302220313012233000332110301", "300023230120321201000232320122000221230223301020233332031221130021112202232302", "111000103321033203222132010311313313031030102131123231133013232112310313012023", "323021112132201033320220311022302203003023030101001332221202111113311222033300", "232120220012203033110011002110132332030131123110030203001213020013130112301111", "133003111210312023111220002130221131303302003312222322122320111111302120000022", "121331010031022313231223331021013122232000332022303301030213131303123132002221", "213101202130101123200300201023223333022330023100133002220031323233310322322222", "102210332111123223003310301333313133023121130033021021231020232330131102222111", "120203303000122330111301230300111000332110320000103202220233133033131330203022", "033132131322230213310233030331231230300201131230223010320131133100031233303301", "211211331131000112210022000330021201010231000203211013111311323121011203322300", "010110302001323200023110112001300113331201302212011313000202301303323302232023", "032300121323020021323322220122123330102032003012133333311311201211322033231022", "321201320102102101012031333030211000313221001203113001331210133310312002102110", "112212100020323112203302110233330213303330021323221203310203031232013113033330", "303101311003333301032323200102130323213020030202101000013003303131123011001003", "112013122220003133232222110120023020103110202331223202333020021113212133030303", "100131203030032112332222332223130030202213110333330313132230103203201002023013", "133011021010121031012111002121310023322220001032312332222031231033111221303130", "121023012233230333321030313001220310200330021233203111220111121331020031003102", "032120332002111122013230131021111212111123232112220220100301333203123032121022", "121300111221101300100201122233032330100010303301113111312033323032002132221321", "311321130102123100120011213301200120322001320222133033321333103321131223111112", "030120333201312033123133102320102332131000110230100222113111112131323331233121", "022203121131313323322113122122203131303113303001111302202321322131023032033330"]); G:=MatrixGroup<78,F|x,y>; print "Group G is E6(4) < GL(78,GF(4))";