/* www-ATLAS of Group Representations. 22.Sz(8):3 represented as 120 x 120 matrices over GF(7). */ F:=GF(7); x:=CambridgeMatrix(1,F,120,[ "000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "260600400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "010000500020000106000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "431106300000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "500652055635306502605334031254600415225100000000000000000000000000000000000000000000000000000000000000000000000000000000", "650400600020000006000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "562005000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000", "005346125350155320630415415305561204561600000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "035060306545655564565626431262224401116100000000000000000000000000000000000000000000000000000000000000000000000000000000", "025102300000000310000000600000000000200000000000000000000000000000000000000000000000000000000000000000000000000000000000", "234234651001301314616261021154263442534000000000000000000000000000000000000000000000000000000000000000000000000000000000", "401540633165235200065062535516033204216200000000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "012604400000000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "532403601531632403001015236542241536221100000000000000000000000000000000000000000000000000000000000000000000000000000000", "622542023524065250546214244541143040220400000000000000000000000000000000000000000000000000000000000000000000000000000000", "113024616410120341534121053535546332503500000000000000000000000000000000000000000000000000000000000000000000000000000000", "604325543423123001500206323311035025530500000000000000000000000000000000000000000000000000000000000000000000000000000000", "115430421651133114215663144022560345505100000000000000000000000000000000000000000000000000000000000000000000000000000000", "260066033042426004524065256426230262551600000000000000000000000000000000000000000000000000000000000000000000000000000000", "360000620010600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000", "514163151260350531336313524600541002025000000000000000000000000000000000000000000000000000000000000000000000000000000000", "266501233143004315160316310403031306625500000000000000000000000000000000000000000000000000000000000000000000000000000000", "021066632042522140062221223433320541514500000000000000000000000000000000000000000000000000000000000000000000000000000000", "403343550243134415551135601253205166414600000000000000000000000000000000000000000000000000000000000000000000000000000000", "535461566601143465060343326541654424246500000000000000000000000000000000000000000000000000000000000000000000000000000000", "422403343404613003255223055635536663541300000000000000000000000000000000000000000000000000000000000000000000000000000000", "602633202226220541564133161312415006122400000000000000000000000000000000000000000000000000000000000000000000000000000000", "066554342432432122615425441161354344245000000000000000000000000000000000000000000000000000000000000000000000000000000000", "346533203635145166040052504516415455304200000000000000000000000000000000000000000000000000000000000000000000000000000000", "305523651244003011166144420136011230320300000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "456655444402231446563544013015501136416000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000035030030000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000040040020006000020600000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000050220620000000060000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000033455012161422153006253000645165252522550000000000000000000000000000000000000000", "000000000000000000000000000000000000000045040010005000000500000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000046500100000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000000000020626641610055055561165450441256055435020000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000046320115521220064003663600365420234434660000000000000000000000000000000000000000", "000000000000000000000000000000000000000024430530000000022000000060000000000060000000000000000000000000000000000000000000", "000000000000000000000000000000000000000054411420030235032415000441233655112255220000000000000000000000000000000000000000", "000000000000000000000000000000000000000033633240156146444424464664023351543105110000000000000000000000000000000000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000025310510000000006000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000063632143010301304165463361251122103335250000000000000000000000000000000000000000", "000000000000000000000000000000000000000005401513534333065211431565422461306662250000000000000000000000000000000000000000", "000000000000000000000000000000000000000056006123333442436654464340210312131544050000000000000000000000000000000000000000", "000000000000000000000000000000000000000015226502154204445362352015215306051125310000000000000000000000000000000000000000", "000000000000000000000000000000000000000010543132452040536243414345252630601654450000000000000000000000000000000000000000", "000000000000000000000000000000000000000040261032650303250534414052665211350201300000000000000000000000000000000000000000", "000000000000000000000000000000000000000000050036002060000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000000000000000000000023613355233630465614333305555222425600020000000000000000000000000000000000000000", "000000000000000000000000000000000000000010341630143022266215665454026046301303110000000000000000000000000000000000000000", "000000000000000000000000000000000000000012062126540064524213001513010355020023300000000000000000000000000000000000000000", "000000000000000000000000000000000000000063535566641033161243640360134261152121660000000000000000000000000000000000000000", "000000000000000000000000000000000000000001511330354623625323551465316250423356100000000000000000000000000000000000000000", "000000000000000000000000000000000000000022620300642542566054412462012312066633110000000000000000000000000000000000000000", "000000000000000000000000000000000000000044410055665331043553653146452566426346440000000000000000000000000000000000000000", "000000000000000000000000000000000000000010556442256160665535142014410432440143410000000000000000000000000000000000000000", "000000000000000000000000000000000000000024306321312334542502530633446264605112100000000000000000000000000000000000000000", "000000000000000000000000000000000000000000226115454464364234445464104231515221240000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000033342332225054151650622503110640016464040000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000006301006000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000001506005000100003060000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000001544063000000006000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000002100033531206223261000050055200525514116", "000000000000000000000000000000000000000000000000000000000000000000000000000000005302006000400000030000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000005640060000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006000", "000000000000000000000000000000000000000000000000000000000000000000000000000000006220600160252260620120513320615035655552", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000004150014532211406303564603422453400543150", "000000000000000000000000000000000000000000000000000000000000000000000000000000004560020000000003300000001000000000006000", "000000000000000000000000000000000000000000000000000000000000000000000000000000003650261664400452625025141063541550556104", "000000000000000000000000000000000000000000000000000000000000000000000000000000005424121203062651366613445504411641356102", "000000000000000000000000000000000000000000000000000000000000000000000000000000006000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000002511036000000000100000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000005340462053536334231115321541203511100303", "000000000000000000000000000000000000000000000000000000000000000000000000000000005264332415641605320412431054613325241662", "000000000000000000000000000000000000000000000000000000000000000000000000000000000044260415003636652142102131414521116141", "000000000000000000000000000000000000000000000000000000000000000000000000000000003051453344332441452335210544263212165511", "000000000000000000000000000000000000000000000000000000000000000000000000000000000553116501342563226215033233553525645311", "000000000000000000000000000000000000000000000000000000000000000000000000000000005535644462001066501224556550456263302210", "000000000000000000000000000000000000000000000000000000000000000000000000000000006504005600401000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000000000006544514351412232434235044432250054534306", "000000000000000000000000000000000000000000000000000000000000000000000000000000006034503024640565540442136601153460230536", "000000000000000000000000000000000000000000000000000000000000000000000000000000001440663031312632604421266334536025366305", "000000000000000000000000000000000000000000000000000000000000000000000000000000003524356513155030101461133053002540202033", "000000000000000000000000000000000000000000000000000000000000000000000000000000001522621416544422215615256240362124216111", "000000000000000000000000000000000000000000000000000000000000000000000000000000001510500065426454253662136130212444003323", "000000000000000000000000000000000000000000000000000000000000000000000000000000006606346014166443031506215606654606252506", "000000000000000000000000000000000000000000000000000000000000000000000000000000006606653533052226460252521441414035446324", "000000000000000000000000000000000000000000000000000000000000000000000000000000006005221640230030013346026642440403510330", "000000000000000000000000000000000000000000000000000000000000000000000000000000005131412165406102032454346244030436511604", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000600000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000004040540143602356156024115016545111511612"]); y:=CambridgeMatrix(1,F,120,[ "000000000000000000000000000000000000000010112255524331663503510301614405112350210000000000000000000000000000000000000000", "000000000000000000000000000000000000000021052421665544442450621566116560162523300000000000000000000000000000000000000000", "000000000000000000000000000000000000000022544234201313601431336453016612101045530000000000000000000000000000000000000000", "000000000000000000000000000000000000000022064565003112030503052554544631100460130000000000000000000000000000000000000000", "000000000000000000000000000000000000000051002101554316266001615405256260042421160000000000000000000000000000000000000000", "000000000000000000000000000000000000000040233042465200352022503301054624661431450000000000000000000000000000000000000000", "000000000000000000000000000000000000000035521632305344332531146206252332046432200000000000000000000000000000000000000000", "000000000000000000000000000000000000000052545020225506022654243522253612362263610000000000000000000000000000000000000000", "000000000000000000000000000000000000000016300463060150203006356131005442215362550000000000000000000000000000000000000000", "000000000000000000000000000000000000000045552400126145144154433453562246134655610000000000000000000000000000000000000000", "000000000000000000000000000000000000000055516602316315330153626146260140420565200000000000000000000000000000000000000000", "000000000000000000000000000000000000000004133224363432450426051656505026214040350000000000000000000000000000000000000000", "000000000000000000000000000000000000000032516136012106116066045052353410101443410000000000000000000000000000000000000000", "000000000000000000000000000000000000000051515623500653116014540443413060465251010000000000000000000000000000000000000000", "000000000000000000000000000000000000000052206151154141453021052432424653155246440000000000000000000000000000000000000000", "000000000000000000000000000000000000000041533343653242130304255005553402422441230000000000000000000000000000000000000000", "000000000000000000000000000000000000000062213616323426141362035444401555311264020000000000000000000000000000000000000000", "000000000000000000000000000000000000000023314122216546031340545454451444120205100000000000000000000000000000000000000000", "000000000000000000000000000000000000000036012625566126126003014325226300145653240000000000000000000000000000000000000000", "000000000000000000000000000000000000000045450450514614220132166650365531401210600000000000000000000000000000000000000000", "000000000000000000000000000000000000000030520052220666215345502446154526120120060000000000000000000000000000000000000000", "000000000000000000000000000000000000000010404343233532653266560014560631666555430000000000000000000000000000000000000000", "000000000000000000000000000000000000000016213352414332110602356220161546044456520000000000000000000000000000000000000000", "000000000000000000000000000000000000000015462240254353351604144102042061126026000000000000000000000000000000000000000000", "000000000000000000000000000000000000000050224654121314542641050536460425130156450000000000000000000000000000000000000000", "000000000000000000000000000000000000000063060646211615563322143430442536304601250000000000000000000000000000000000000000", "000000000000000000000000000000000000000054140642301101553205360360436052024021520000000000000000000000000000000000000000", "000000000000000000000000000000000000000014430233222034554261124140646626536510220000000000000000000000000000000000000000", "000000000000000000000000000000000000000044225250342333104452536345545431563240200000000000000000000000000000000000000000", "000000000000000000000000000000000000000021625360023416615620302226610653262562550000000000000000000000000000000000000000", "000000000000000000000000000000000000000045524505161525134531461620425131530311310000000000000000000000000000000000000000", "000000000000000000000000000000000000000044133152253446606124354025556524232543240000000000000000000000000000000000000000", "000000000000000000000000000000000000000045133521315216635214526422614244610113510000000000000000000000000000000000000000", "000000000000000000000000000000000000000044442554334065622460322404600400314626510000000000000000000000000000000000000000", "000000000000000000000000000000000000000034153100165563565143301420053026205402550000000000000000000000000000000000000000", "000000000000000000000000000000000000000052564324512065235020624463542555542035110000000000000000000000000000000000000000", "000000000000000000000000000000000000000021214652330453122453663445521662453224430000000000000000000000000000000000000000", "000000000000000000000000000000000000000016620406430523536052221062105510614512360000000000000000000000000000000000000000", "000000000000000000000000000000000000000062543020560001260416566641455534306612330000000000000000000000000000000000000000", "000000000000000000000000000000000000000025023561663311123261633154035013520140310000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000002566624415154005366251620621643333654160", "000000000000000000000000000000000000000000000000000000000000000000000000000000002041332651610621234111430562404233542630", "000000000000000000000000000000000000000000000000000000000000000000000000000000005543052212532163640556206026032224321436", "000000000000000000000000000000000000000000000000000000000000000000000000000000000205026100620624055133413165155405613033", "000000000000000000000000000000000000000000000000000000000000000000000000000000001441356350622665312053611600560325635134", "000000000000000000000000000000000000000000000000000000000000000000000000000000000423206065445554015252221251223546246226", "000000000000000000000000000000000000000000000000000000000000000000000000000000003102533653355436405101440064635130342004", "000000000000000000000000000000000000000000000000000000000000000000000000000000004526531224051064641406464342012353066603", "000000000000000000000000000000000000000000000000000000000000000000000000000000005232155000541266305163365024262513460202", "000000000000000000000000000000000000000000000000000000000000000000000000000000002306125023140412312243415661651055132246", "000000000000000000000000000000000000000000000000000000000000000000000000000000005224445651431026605243343651113454636512", "000000000000000000000000000000000000000000000000000000000000000000000000000000001064121124153330435213521403366345400360", "000000000000000000000000000000000000000000000000000000000000000000000000000000003134202133512520004132650335632345124155", "000000000000000000000000000000000000000000000000000000000000000000000000000000001362553432323213514236511330523325031141", "000000000000000000000000000000000000000000000000000000000000000000000000000000003265106346251345215513602450260551541435", "000000000000000000000000000000000000000000000000000000000000000000000000000000000461314052604242532240131215616150110606", "000000000000000000000000000000000000000000000000000000000000000000000000000000004215241455441462526145622124215540320123", "000000000000000000000000000000000000000000000000000000000000000000000000000000001322516555500402032145341501625204265211", "000000000000000000000000000000000000000000000000000000000000000000000000000000001621052543231340516434630454655263355516", "000000000000000000000000000000000000000000000000000000000000000000000000000000005663615311224011042063135015521224352314", "000000000000000000000000000000000000000000000000000000000000000000000000000000002103021115043661543102151552215540536634", "000000000000000000000000000000000000000000000000000000000000000000000000000000002516656541663633565615035501214152320530", "000000000000000000000000000000000000000000000000000000000000000000000000000000006150114454426134444531666615022602203215", "000000000000000000000000000000000000000000000000000000000000000000000000000000000425501426526255162643213331541520506632", "000000000000000000000000000000000000000000000000000000000000000000000000000000003463513210440653063200453403046164210041", "000000000000000000000000000000000000000000000000000000000000000000000000000000001153652230104233221142441215322665535533", "000000000000000000000000000000000000000000000000000000000000000000000000000000003143254461531313626443643005562622364554", "000000000000000000000000000000000000000000000000000000000000000000000000000000002260653446334410004061044641252056443105", "000000000000000000000000000000000000000000000000000000000000000000000000000000005322100645131052403010306662306414322035", "000000000000000000000000000000000000000000000000000000000000000000000000000000004351014435556420461423305002203146165160", "000000000000000000000000000000000000000000000000000000000000000000000000000000003161166046561434160326045120400006302536", "000000000000000000000000000000000000000000000000000000000000000000000000000000004325065206566414422423216204416556605055", "000000000000000000000000000000000000000000000000000000000000000000000000000000003255111111240142043561341400335051045444", "000000000000000000000000000000000000000000000000000000000000000000000000000000002114011002101264406410535254545162144611", "000000000000000000000000000000000000000000000000000000000000000000000000000000003164524105436553304162166602662432643513", "000000000000000000000000000000000000000000000000000000000000000000000000000000003460432165034263514002342032422433514535", "000000000000000000000000000000000000000000000000000000000000000000000000000000003200421250654216052353224545244455603415", "000000000000000000000000000000000000000000000000000000000000000000000000000000000165240432253440565443655021464444025600", "000000000000000000000000000000000000000000000000000000000000000000000000000000005304234605552325236240522361031665536546", "000000000000000000000000000000000000000000000000000000000000000000000000000000000411514115345651330326323115053632330633", "046135366046136234312154242335502512661400000000000000000000000000000000000000000000000000000000000000000000000000000000", "445322442422610630361110324135361063161500000000000000000000000000000000000000000000000000000000000000000000000000000000", "163120312054463120034155301165500411154100000000000000000000000000000000000000000000000000000000000000000000000000000000", "236356335523126365364426603534105165354100000000000000000000000000000000000000000000000000000000000000000000000000000000", "465536206504416514642232320024652200222000000000000000000000000000000000000000000000000000000000000000000000000000000000", "546040450412043065354153553505632551412000000000000000000000000000000000000000000000000000000000000000000000000000000000", "065022453402364154006315434352131512531500000000000000000000000000000000000000000000000000000000000000000000000000000000", "143300021012151440130660101100146016363500000000000000000000000000000000000000000000000000000000000000000000000000000000", "000423311264201525301141612641064543001300000000000000000000000000000000000000000000000000000000000000000000000000000000", "622046644043523251153003300325362066556400000000000000000000000000000000000000000000000000000000000000000000000000000000", "552002366241331554336363610606464005415500000000000000000000000000000000000000000000000000000000000000000000000000000000", "311500514466434411062153304416421016345400000000000000000000000000000000000000000000000000000000000000000000000000000000", "552316062624350356332334210425020406613400000000000000000000000000000000000000000000000000000000000000000000000000000000", "400013523151140536454014505665345160345300000000000000000000000000000000000000000000000000000000000000000000000000000000", "015563455200343612060301643034532512142100000000000000000000000000000000000000000000000000000000000000000000000000000000", "440245303645514335416502543132605066225400000000000000000000000000000000000000000000000000000000000000000000000000000000", "262143651364440050522405360463263654146300000000000000000000000000000000000000000000000000000000000000000000000000000000", "061654513412214263424236133312561034300300000000000000000000000000000000000000000000000000000000000000000000000000000000", "513262443601041050056664010025405004564500000000000000000000000000000000000000000000000000000000000000000000000000000000", "650662163611333155224231324122264333551300000000000000000000000000000000000000000000000000000000000000000000000000000000", "134166265315252530004262354113212512043500000000000000000000000000000000000000000000000000000000000000000000000000000000", "650520263254665311360310353615634536143000000000000000000000000000000000000000000000000000000000000000000000000000000000", "542332364613114216203351424455114661104500000000000000000000000000000000000000000000000000000000000000000000000000000000", "414466342311614155360432156060061413216300000000000000000000000000000000000000000000000000000000000000000000000000000000", "340346004111365003213521604012051532665300000000000000000000000000000000000000000000000000000000000000000000000000000000", "011331253612321525463622424232530540111000000000000000000000000000000000000000000000000000000000000000000000000000000000", "512314324431424415020416046401130256423400000000000000000000000000000000000000000000000000000000000000000000000000000000", "244322040400151231622023250646436643644300000000000000000000000000000000000000000000000000000000000000000000000000000000", "003153422311044035255025321201420546064200000000000000000000000000000000000000000000000000000000000000000000000000000000", "165540165145521355024210512420010223413200000000000000000000000000000000000000000000000000000000000000000000000000000000", "121025250521032541000362461662540156102000000000000000000000000000000000000000000000000000000000000000000000000000000000", "660645510461205564364143502016020116413300000000000000000000000000000000000000000000000000000000000000000000000000000000", "545144032533206361302442655366565352035400000000000000000000000000000000000000000000000000000000000000000000000000000000", "064041524552621024036146530661046063305600000000000000000000000000000000000000000000000000000000000000000000000000000000", "541024045126154433002040442540400515453500000000000000000000000000000000000000000000000000000000000000000000000000000000", "006334314462112245005335165323120215606100000000000000000000000000000000000000000000000000000000000000000000000000000000", "542645511562250641632015400351461064526100000000000000000000000000000000000000000000000000000000000000000000000000000000", "461514566252122525101513350214526464014400000000000000000000000000000000000000000000000000000000000000000000000000000000", "356440621355162453511502500314561563216000000000000000000000000000000000000000000000000000000000000000000000000000000000", "560544052554265352032166640346604660552200000000000000000000000000000000000000000000000000000000000000000000000000000000"]); G:=MatrixGroup<120,F|x,y>; print "Group G is 22.Sz(8):3 < GL(120,GF(7))";