/* 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", 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"2430342230130042210243411010304421101232243021033321442241120332134021012100", "0000000000000000000000000000000000000000000000000000000000010000000000000000", "0000000000000000000000000000000000000000000000000000000000000010000000000000", "0000000000000000000000000000000000000000000000000000000000000000010000000000", "4111414313012003432414022122043444003400404214332320304040434440304013004341"]); y:=CambridgeMatrix(1,F,76,[ "0010000000000000000000000000000000000000000000000000000000000000000000000000", "0001000000000000000000000000000000000000000000000000000000000000000000000000", "0114000000000000000000000000000000000000000000000000000000000000000000000000", "4110000000000000000000000000000000000000000000000000000000000000000000000000", "0000001000000000000000000000000000000000000000000000000000000000000000000000", "0000000100000000000000000000000000000000000000000000000000000000000000000000", "0330404000000000000000000000000000000000000000000000000000000000000000000000", 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"0000000000000000000000000000000000000000000010000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000000000000000001", "1243342302243323023303443131200431204224424023133012134402211440242441421033", "1012111122413132022330022304313001441030234141432100102231123144004131431334", "2121432431204242142244321443302230100434022120122424313024001001234202144310", "4023243400004223204033042241111332324121240141124344343310432332304110444210", "4311013323002142420340433132230214134400120021204004440344033243100040040432", "0334404402002011231324304444400204041402423101143244434432014100042132441044", "0000000000000000000000000000000000000000000000000000000100000000000000000000"]); G:=MatrixGroup<76,F|x,y>; print "Group G is J1 < GL(76,GF(5))";