/* www-ATLAS of Group Representations. O8-(2) represented as 84 x 84 matrices over GF(5). */ F:=GF(5); x:=CambridgeMatrix(1,F,84,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000000000", 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"411023104441001333321304320324010401021020020122113213424140314003343122411002023404", "000000000000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000000000", "421100232203014003131443440032010142210423213011412140031333412041112233201303421133", "000000000000000000000000000000000000000000000000000010000000000000000000000000000000", "412033411121033224111002414221044010023230210241001203442230231222214330130431003033", "300404414102231100121103000442032404233421224013422310403424400120013342231440214024", "000000000000000000000000000000000000000000000000000000100000000000000000000000000000", "423043240024423234444310443414441302410113102423341224441231314341312123422302410321", "203210413313222230422320422122101032413000343242413303430443124033424442214123323322", "432410112141432034030141234204314344444221430002324003124203131104021031332141340404", "000000000000000000000000000000000000000000000000000000000100000000000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000000000000", "040103331312210222230032234023013314411402114232122232204414301131404132240121221333", "320024041440031403133433142144034312403130420401220340411043230242242403021321021223", "322323114431124143134024022401330431404232211011100242034330404000030100000022001000", "000000000000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000000000000", "022300331014103110342402423112440431420311404111213000312423002303014300421024314124"]); y:=CambridgeMatrix(1,F,84,[ "100000000000000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000000000", "444000000000000000000000000000000000000000000000000000000000000000000000000000000000", 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"000000000000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000010000000000000000000000000000000000000000000000000", "202020411341330014232240004341121010213044234102123102433011202333100304022230044000", "000000000000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000000000001", "120240404024114303200230114123411124414211434213320123233044040302122413301043304101", "100223230202344320342130331300112442420130224440211240334230041034344021301012014420", "342301200122310033012021213444001034330140412104032021423344341221200111140313210102", "000000000000000000000000000000000000001000000000000000000000000000000000000000000000", "110023203030140344412400401310410331403121313043321233214322234032421301120310210341", "000000000000000000000000000000000000000100000000000000000000000000000000000000000000", "321244434033111340242033224442320333434323041014441403012313402002204000003213244314", "023012303241132330322214422220223344043210341102031032020411204112442044422404010230", "000000000000000000000000000000000000000001000000000000000000000000000000000000000000", "142042210400333403302410412243304220140323322433023300433000403004320224424330334402", "020430424210123114242001334344331040232400413314444420314112022103342303021140023214", "321332421130430231103131443033403224314033043020112334243220202221432233433031020322", "234211310031033444341000432032420040142110342034002420324400203011133030104403430210", "000000000000000000000000000000000000000000001000000000000000000000000000000000000000", "342103141101314422134330241334011334440414014202330423004124202120300033411313202433", "333202444143431021412330121414442133021340013042314424000203420402202412323401222224", "142212001020424303420344404421041401241030321224111443040302443044244233344023414012", "100304440043104244033010210231302243111102212130310240042012043041204011244340421113", "000000000000000000000000000000000000000000000000100000000000000000000000000000000000"]); G:=MatrixGroup<84,F|x,y>; print "Group G is O8-(2) < GL(84,GF(5))";