/* www-ATLAS of Group Representations. M12 represented as 78 x 78 matrices over GF(5). */ F:=GF(5); x:=CambridgeMatrix(1,F,78,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000010000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000001000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000010000000000000000000000000000000000000000000", "000000000000000000000000000000000001000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000001000000000000000000000000000000000000000", "000000000000000000000000000000000000000100000000000000000000000000000000000000", "000000000000000000000000000000000000000001000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000000", "000000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000001000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000100000000000000000000000000000000000", "000000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000010", "441244003232140022003323321211202114030112201032111130012424400022411333430020", "000000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000010000000000000000000000000000000", "210141231022321134122303223440230044304120221230440043412234433343440021231110", "000000000000000000000000000000000000000000000001000000000000000000000000000000", "124043241202103040031332232134341034102431433103442114140144043424223423022102", "034204403213043204222041202434411301244403213244130213110134121123403002042402", "440334241022134204440404302140210024040442141134414130310323440343200134444143", "000000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000", "421324042432230202301302012104302341120222411313200430422322412110301140444340", "000000000000000000000000000000000000000000000000000010000000000000000000000000", "031230122113411021204320404411322132001110212400113330043133314443013421310422", "000221343104104441311344434320324020114034143341032423224003034201301011311033", "000000000000000000000000000000000000000000000000000000100000000000000000000000", "214414113411433040413310121041442031242024241213102203141221200124433202412000", "024234101331124334313433033413443113142012240400120222211304214224433331421403", "022310111404223422232012201122103144322002100014311131302431342104402024103302", "000000000000000000000000000000000000000000000000000000000100000000000000000000", "420024340331442034312112313143322412340344421443044414233432310021211341032130"]); y:=CambridgeMatrix(1,F,78,[ "001000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "432200000000000000000000000000000000000000000000000000000000000000000000000000", "421400000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000", "102240400000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000100000000000000000000000000000000000000000000000000000000000000", "000000000000000001000000000000000000000000000000000000000000000000000000000000", "000000000000000000100000000000000000000000000000000000000000000000000000000000", "000000000000000000010000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000100000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000100000000000000000000000000000000000000000000000000000", "000000000000000000000000001000000000000000000000000000000000000000000000000000", "000000000000000000000000000100000000000000000000000000000000000000000000000000", "000000000000000000000000000001000000000000000000000000000000000000000000000000", "000000000000000000000000000000100000000000000000000000000000000000000000000000", "000000000000000000000000000000010000000000000000000000000000000000000000000000", "000000000000010000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000001000000000000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000", 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"000000000000000000000010000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000100000000000000000000000", "000000000000000000000001000000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000001", "201222041034314013333312302010421302201103212040343004221100231312323330112132", "420433443332221142432412311424204230403203140032411103242142023020403232220001", "000000000000000000000000000000000010000000000000000000000000000000000000000000", "041203134141310133030014221111141312301304343213013213410442024024111040034022", "000000000000000000000000000000000001000000000000000000000000000000000000000000", "341422342421314043441040144012114242400111043143131340334111240332022240204133", "041414010442230002022202110041432103144300320133110233413331333221144312242400", "431332020423242104444412401301434101411042122114120412004143204232003341012142", "000144421202314121301001311120024003334303333120432313020212301004344200402412", "000000000000000000000000000000000000001000000000000000000000000000000000000000", "422434443344311322042032130033010301243013012332233143321102233331441212044300", "000000000000000000000000000000000000000100000000000000000000000000000000000000", "334002400232433410410311341200421213003121023224331124220230201422114040142402", "132114220312330244142021224002440001141131423211014203022003242344442100031103", "000000000000000000000000000000000000000001000000000000000000000000000000000000", "240202012341003103103022333312003001342341304124010001024340143004340223444323", "302413213330243101423200104400422303244414222400243134302013444411444404441221", "433102421031221020014323433132014412030122244114222411431223343024302314401321", "000000000000000000000000000000000000000000001000000000000000000000000000000000"]); G:=MatrixGroup<78,F|x,y>; print "Group G is M12 < GL(78,GF(5))";