/* www-ATLAS of Group Representations. J1 represented as 76 x 76 matrices over GF(5). */ F:=GF(5); x:=CambridgeMatrix(1,F,76,[ "0100000000000000000000000000000000000000000000000000000000000000000000000000", "1000000000000000000000000000000000000000000000000000000000000000000000000000", "0000100000000000000000000000000000000000000000000000000000000000000000000000", "0000010000000000000000000000000000000000000000000000000000000000000000000000", "0010000000000000000000000000000000000000000000000000000000000000000000000000", "0001000000000000000000000000000000000000000000000000000000000000000000000000", "0000000010000000000000000000000000000000000000000000000000000000000000000000", "0000000001000000000000000000000000000000000000000000000000000000000000000000", "0000001000000000000000000000000000000000000000000000000000000000000000000000", "0000000100000000000000000000000000000000000000000000000000000000000000000000", "0000000000000100000000000000000000000000000000000000000000000000000000000000", "0000000000000010000000000000000000000000000000000000000000000000000000000000", "0000000000000000100000000000000000000000000000000000000000000000000000000000", "0000000000100000000000000000000000000000000000000000000000000000000000000000", "0000000000010000000000000000000000000000000000000000000000000000000000000000", "3320320020000400000400000000000000000000000000000000000000000000000000000000", "0000000000001000000000000000000000000000000000000000000000000000000000000000", "0000000000000000000001000000000000000000000000000000000000000000000000000000", "0000000000000000000000100000000000000000000000000000000000000000000000000000", "3332202000400004000000000000000000000000000000000000000000000000000000000000", "4111101000400004000000040000000000000000000000000000000000000000000000000000", "0000000000000000010000000000000000000000000000000000000000000000000000000000", "0000000000000000001000000000000000000000000000000000000000000000000000000000", "3140340040000000000140000000000000000000000000000000000000000000000000000000", "0000000000000000000000000000100000000000000000000000000000000000000000000000", "0000000000000000000000000000010000000000000000000000000000000000000000000000", "0000000000000000000000000000001000000000000000000000000000000000000000000000", "0000000000000000000000000000000010000000000000000000000000000000000000000000", "0000000000000000000000001000000000000000000000000000000000000000000000000000", "0000000000000000000000000100000000000000000000000000000000000000000000000000", "0000000000000000000000000010000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000100000000000000000000000000000000000000", "0000000000000000000000000001000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000001000000000000000000000000000000000000", "0000000000000000000000000000000000000000100000000000000000000000000000000000", 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"0000000000000000000000000000000000000010000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000001000000000000000000", "0000000000000000000000000000000000000000000000000000000000100000000000000000", "0000000000000000000000000000000000000000000000000000000000001000000000000000", "0000000000000000000000000000000000000000010000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000001000000000000", "0000000000000000000000000000000000000000000100000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000000001000000000", "0000000000000000000000000000000000000000000001000000000000000000000000000000", "0000000000000000000000000000000000000000000000100000000000000000000000000000", "0000000000000000000000000000000000000000000000001000000000000000000000000000", "0000000000000000000000000000000000000000000000000100000000000000000000000000", 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"1202313142024112324411031432131114110320212104313143144201132434431303421404", "0000000000000000000000000000000000000000000000000000000000010000000000000000", "0000000000000000000000000000000000000000000000000000000000000100000000000000", "0000000000000000000000000000000000000000000000000000000000000010000000000000", "0000000000000000000000000000000000000000000000000000000000000000010000000000"]); y:=CambridgeMatrix(1,F,76,[ "0010000000000000000000000000000000000000000000000000000000000000000000000000", "0001000000000000000000000000000000000000000000000000000000000000000000000000", "0114000000000000000000000000000000000000000000000000000000000000000000000000", "4110000000000000000000000000000000000000000000000000000000000000000000000000", "0000001000000000000000000000000000000000000000000000000000000000000000000000", "0000000100000000000000000000000000000000000000000000000000000000000000000000", "0330404000000000000000000000000000000000000000000000000000000000000000000000", "0000000000100000000000000000000000000000000000000000000000000000000000000000", "0000000000010000000000000000000000000000000000000000000000000000000000000000", "0000000000001000000000000000000000000000000000000000000000000000000000000000", "0000010000000000000000000000000000000000000000000000000000000000000000000000", "0000000000000001000000000000000000000000000000000000000000000000000000000000", "0000000000000000010000000000000000000000000000000000000000000000000000000000", "0000000000000000001000000000000000000000000000000000000000000000000000000000", "0000000000000000000100000000000000000000000000000000000000000000000000000000", "0000000010000000000000000000000000000000000000000000000000000000000000000000", "0000000000000000000010000000000000000000000000000000000000000000000000000000", "0000000001000000000000000000000000000000000000000000000000000000000000000000", "0000000000000000000000010000000000000000000000000000000000000000000000000000", "0000000000000000000000001000000000000000000000000000000000000000000000000000", "0000000000000000000000000100000000000000000000000000000000000000000000000000", "0000000000000000000000000010000000000000000000000000000000000000000000000000", "0000000000000000000000000001000000000000000000000000000000000000000000000000", "0000000000000100000000000000000000000000000000000000000000000000000000000000", "0000000000000010000000000000000000000000000000000000000000000000000000000000", "0000000000000000100000000000000000000000000000000000000000000000000000000000", "0000000000000000000000000000000100000000000000000000000000000000000000000000", "0000000000000000000000000000000001000000000000000000000000000000000000000000", "0000000000000000000000000000000000100000000000000000000000000000000000000000", "0000000000000000000000000000000000010000000000000000000000000000000000000000", "0000000000000000000000000000000000001000000000000000000000000000000000000000", 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"0000000000000000000000000000000000000000000000000000000000000000000010000000", "0000000000000000000000000000000000000000000000000000000000000000000001000000", "0000000000000000000000000000000000000000000000000000000000000000000000100000", "0000000000000000000000000000000000000000000000000000000000000000000000010000", "0000000000000000000000000000000000000001000000000000000000000000000000000000", "4100400000020300000010000000000000000400000000000004000000000000000000000000", "0000000000000000000000000000000000000000100000000000000000000000000000000000", "4221101020000000100000030000000000000000000000040000000000004000000000000000", "3030330030010400000230000000000000000400000000000004000000000000000000004000", "0000000000000000000000000000000000000000001000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000000001000000000", "0000000000000000000000000000000000000000000000000000010000000000000000000000", "0000000000000000000000000000000000000000000010000000000000000000000000000000", "2142143224431423231231001224333232002302103024334142041310414030300130430141", "4414222134423043033030012033212111134211100424141403134021104213213321440213", "0344402311403010323124313111033133211111011334314420441213404212210331014223", "1420314243423142142341200420340433103301304312030113441001420413200100242032", "1414434433323114104022240342433200320003102100302111013003412142432113411302", "2100304104423221044121310403202303230133204411123102332143333033432004333443", "0432104233031444321140330334402301140223430431334442233024314414212333412034", "3110410321410040232420033410420112043021043404343404304311031004000444342000"]); G:=MatrixGroup<76,F|x,y>; print "Group G is J1 < GL(76,GF(5))";