/* www-ATLAS of Group Representations. M12:2 represented as 78 x 78 matrices over GF(5). */ F:=GF(5); x:=CambridgeMatrix(1,F,78,[ "010000000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000", "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", "334400101010010000000000004000000040000000400000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000100000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000010000000000000000000", "000000000000000000000000000000000000000000000040000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000100000000000000000", "000000000000000000000000000000000000100000000000000000000000000000000000000000", "000000000000000000000000000000000000010000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000100000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000000", "000000000000000000000000000000000000000000000000000000000000000000100000000000", "000000000000000000000000000000000000000010000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000100000000", "000000000000000000000000000000000000000000010000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000010", "000000000000000000000000000000000000000000000001000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000000001", "422230243004413230232144034034431222301110234334132421330233111120020322012114", "000000000000000000000000000000000000000000000000001000000000000000000000000000", "000000000000000000000000000000000000000000000000000100000000000000000000000000", "103132343421301414322230432223303403044040300024234033223201214024403341240002", "000000000000000000000000000000000000000000000000000010000000000000000000000000", "322013442412444024334121331201212202020033131222213023244002004343020404112431", "030442140123134431122420110242440140321311030020002142301224341412111004022303", "000000000000000000000000000000000000000000000000000000100000000000000000000000", "010011221113430343442412212004441324133023241043022441232223143421130324340143", "142134341343201011101333021311401132332410011304342330030140120430420230211344", "000000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000000", "403013004142011431024411114143003244330032431421034232020331033431204342224141", "244100012323311233314220200112020334200201121140120141103014120200442003414112", "000000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000000"]); y:=CambridgeMatrix(1,F,78,[ "100000000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000000", "444000000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000000", "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", "000000000000000000000000000000000000000000000000000000001000000000000000000000", "000000000000000000000000000000000000000000000000000000000100000000000000000000", "000000000000000000000000010000000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000000000000000010000000000000000", "000000000000000000000000000000000000000000000000000000000000001000000000000000", "440400000000000000001000000000000000000000000000400000000000000000000000000000", "000000000000000000000000000010000000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000001000000000000", "000000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000000000000000000001000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000000", "000000000000000000000000000000000000000000000000000000000000000000000001000000", "000000000000000000000000000000001000000000000000000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000010000000000000000000000000000000000000000000", "214032122143231011223400400143430412444340411122441340312043031042034042004130", "000000000000000000000000000000000001000000000000000000000000000000000000000000", "011000400000000000000000000000000000100000000000040000000000000000000000000000", "414020401421032410310002321431320022302201202100331044414131113324320124301040", "413431230030024234020100343440411112342133000014041032302430240133324400033440", "000000000000000000000000000000000000001000000000000000000000000000000000000000", "013044334100301330242032442441140412414144431302210222441300140101142440333123", "000000000000000000000000000000000000000100000000000000000000000000000000000000", "331144323230113132333021143120440123100034211321322440444221443413330131311011", "142044344043421310200214302403111234041241304224020003444143101013020043221441", "000000000000000000000000000000000000000001000000000000000000000000000000000000", "312033413120313341044022230142124402101202004420030341024244212421411221431344", "441112203441412233422030200332114113421431230423042041033113424202430331124440", "011134044024022212314422032210120020101243114011421122221244043321323130041413", "000000000000000000000000000000000000000000001000000000000000000000000000000000", "202340330012404100320311300200320244102240414013311121101010044102330422242420", "302030301403021340322233040234222113312334411211221431342413030311242121132231", "301134224313230114333213330321011244141200111224223432440034133324143204404232"]); G:=MatrixGroup<78,F|x,y>; print "Group G is M12:2 < GL(78,GF(5))";