/* www-ATLAS of Group Representations. O7(3) represented as 78 x 78 matrices over GF(7). */ F:=GF(7); x:=CambridgeMatrix(1,F,78,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000000", "000101110100100000600006000006600000006000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000000", "000006000600000610006000060100006600000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000000", "000001000100000060000600006600000066000000060000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000000", "660102111200161160600666016660600006606000060060000000000000000000000000000000", "666062011200101160000000016600000000060000060000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000", "111615656500506610100001061100160000001600010000006000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000000", "111616656666566606166661060000160606001000600000006000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000", "221413445306405510260002052110260000002000026010006000000000000000000000000000", "660002011200101160000000016660000000000000060660000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000000", "444342362203662230033360624330020303000063040036602000000000300000060200000003", "222521534166364426266062043210260600002001030010066000000000100000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000", "555252242202412260422314025660420203004005050060002600000000500000000600000002", "110605666500616010001110001100000101000000010000000060000000000000000000000000", "445356353601503350510005034560510000005000040060001006000000000000000000000000", "221613645300405520100001052210100000001000020010000000600000000000000000000000", "444344304413014351332312035560330203002005050060003000060000500000000600000002", "556263232311302261610005026600610000005000060000001000006000000000000000000000", "555254242411412301510115135060510001005010050060001000000600000000000000000000", "000000000000000000001000000000000100000000000000000000000060000000000000000000", "220603655310515631000110162300000001000010020000000000000006000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000000", "111616645605405610355503061110350505003002010016005000000000260000060100000005", "556263232311302201510105026060510001005000060060001000000000006000000000000000", "665254231411311201510015025060500000005006050060000000000000600600000000000000", "334443403303063330033366034330030303006004040036003000000000400060060200000003", "555252233202303360322204135650330202004016050050003000000000600006000600000002", "112620646005466600355463061010350504003002010016005000000000200000660100000005", "000000000000000000000000000000000000000000000001000000000000000000000000000000", "664146142603412100233512116050240305002014060051004000000000400000016500000004", "555252242202402250322203025550320202003005050050002000000000500000000600000000", "113631635104365500544265651020530402005063010026003000000000300000060260000003", "111616656606506520265602051210260506002001010010006000000000100000000106000005", "556263243302403140422104615460420201004065050061002000000000500000010600600002", "221514535466305606161602061000160106002000010000006000000000000000000000060000", "664045031552301105222504116060240205004016060061004000000000600000010600006002", "660102111200101050000600606500000006000066060000000000000000600000000000000600", "221514545466465516266661052110260606001000020010006000000000000000000000000060", "666161121101201160511105016660510101005006060060001000000000600000000600000001"]); y:=CambridgeMatrix(1,F,78,[ "342064321264065166431511461550264035046324010160225664360103166640662612153411", "556445316431351500444364513601302330046225021460351505454554211605214644412141", "000000006000010000000000000000000000000000000001100000000000000001000006000006", "333121002263264535356503562664432133636444561050554555156416263215340544652343", "121064555535606666011200100221611161126100612201011661100601010160160000166060", "012310464306143213241164166216666460314213365265520452566163624343445521654513", "106241226114511456262366536340532462520544534044141330121052211236206355604162", "336220502412012156433505456220540412565112533223202115511066300214161200160604", "614004354054112222232200422516635564215004154366524555355152612456436613623322", "212236064133335635525610324111601011461246044066652111355614143026250656642153", "355120536504511004364155356224362462653634005553142112110335416651345516431125", "022316006540602415311220364125252102646125646605253113423111063601155133566222", "060213035332234024626503412034356312666425341366222015312363315635646630640530", "301541663054332526453200252603216134323125504615115223011460264454655041552331", "125510044340436355102406002445132316534122544545350336134326652013246434551335", "254611016025055225016114626053206443625354446545223224122460166542065541662434", "336014345641216020600214426642411653114500045030662452256500160664115306610661", "016052560350666026620315150301526063505606411001512551665666506066166060065551", "240024215423624210113360164102436620022552251341666116105515303235013432305341", "130024536505066132223566020112540616111430461351656110165504262124112430106140", "103566063104163306146500461424550146166540151032564553555220112236603321302441", "304245652130441235142400113002126144433556461201424442144561415061650051052550", "410403125165434432042005042616435451335006241264431440545004612355236613631521", "566614565133652300401102306034554164000416426655454341255445530211313442422035", "034064646452542463261004142245602424252433241432654543656310601335112235126343", "040206405505356221340060660024151341055534152244061660456416111431103330265342", "646436046305533303346502305511334630333331221051631015660653062015333462246164", "600206032420321060302403432400500260516166551302020060100101526223601001106101", "660036415630331205636006254625103220532435411301651544056416261310330644632232", "055145636204463523246262664011244511544532222040542601200664212013333461356363", "161264310101111601600616616056021216155224162062366226623106001101210626013012", "504543320510341363034510044535132534445441324123464330254200413216246344046220", "503566523260211565522565315601316053026651556665323442254601616664666051064050", "054405545016246303432315215352151142265454101226563444355650560651224204432452", "241600612502625306515214531535423445433232003404045663066124265556453114341516", "136102561103221252660661124404510166433236556124256555542315063504120220025223", "532026014046536133615065253301322300506224454003440320444625405544343165345605", "366600022035553220626005205203231202030360266532051105166315162240013332365343", "136311615354100420030004665456342430042012110301541554234224145432462004051510", "163034630414050451644600402414636533254103205425203334511310261000011111002125", "636543612202462150122663026325050331346224232516262336532206462065110116013014", "454002032431261326106000110546056510451461065215600606455666060500660161065566", "612236101555154162525300200005142126144446222304056542566306411335222035210330", "360362663234403056643363453452366043525126160212205342012500455253566041563550", "125255006430432402261506262213532554331662333113154601400416003424322145211345", "410326602033213260413211446044031651645352111603660551355216402235112131304230", "524143426400035144122412222262120155325506202263524441055460416113650051252551", "502464541152231426622504201561456152516446062414403451634600566465660051664660", "351160030416546453250504612606555365203603335165526460345052603334535611533211", "104124145455526512044601463526010420265663315625251334501106450601001200662022", "540162054601452042605400125162635401033554320531420450433460115664531344226443", "241533641465115432152206414336605621105223011320540066306162323650426224132315", "044115360426446156416011324563266432634333536156212224322461005554665551562444", "614401512411010326621664351102416653626550516605313443244600606664666051604651", "166331312262013003065414125450611406364061311040066603300060201664125414532604", "264526141240326434042160133432616162311456451646412550444466465651630442032440", "022036044625405105431515020124242002423240041622641102565232556355353310340514", "034365315061405235321161450403310024336566426200314224244401515606656050003641", "600652405555333312040115223305305313403235246145521561406063615343445522053423", "612422335052022202425461164225044005410200256004335452564163124332435012642416", "212000106561610561501006600120011260216216101461160101222011010110010616012211", "636422130663303024252463202160224110316550525234220661543610206466450354051653", "230232325425263056544664254200436315605664636425514061065006200506660262005064", "362044603053562345243006105602126246422444466100415332134561205660666651663543", "204561135546664340366666316525506145653225601642204433331305500113101311162013", "366131220456560352350364452026421125461420123361364326243300211310120626025222", "516134064524234201324606516264501633243551013063502434665316312322221036225321", "604320520661353600116306444016633524253321634104044654466324265644562013153610", "202016146516516531265603052216210616261211111000166110021100201006110016012116", "363531351466422314612440136425121410410642130053120524040123311043316516531525", "661250164366435531265166441123060410331653065344301326655612306660015465530164", "454523235661064150566113510032360452615462044636301443254560006403615460615656", "351062613355043305405524460130406533513352530002214124023553463035453110363212", "355341323204024110055506504422130534031643056561665551256662315001600566666002", "646404330451032152204305032103523313162411636656322341543051564061602001165350", "332144536306140521656203022462601635016060631441616443460001216205116405621066", "220145530056250661344011135240140304161563125455605601056006351664016506510603", "566565232211023452651552426142411661016641213002162100200625502536213540211340"]); G:=MatrixGroup<78,F|x,y>; print "Group G is O7(3) < GL(78,GF(7))";