/* www-ATLAS of Group Representations. J1 represented as 75 x 75 matrices over GF(7). */ F:=GF(7); x:=CambridgeMatrix(1,F,75,[ "010000000000000000000000000000000000000000000000000000000000000000000000000", "100000000000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000", "000001000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000001000000000000000000000000000000000000000000000000000000000000000000", "000000000100000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000000000000100000000000000000000000000000000000000000000000000000000000000", 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"041634005144534561352432133222041316013243056003600211214416122566120262655", "243636541565004165026334513144333544610301304241621501463624260206636134121", "425501312415131310006365536212245304541455540422014614534335625263641555105", "000000000000000000000000000000000000000000000000000000000000100000000000000"]); y:=CambridgeMatrix(1,F,75,[ "610000000000000000000000000000000000000000000000000000000000000000000000000", "001000000000000000000000000000000000000000000000000000000000000000000000000", "261000000000000000000000000000000000000000000000000000000000000000000000000", "000010000000000000000000000000000000000000000000000000000000000000000000000", "000000100000000000000000000000000000000000000000000000000000000000000000000", "000000010000000000000000000000000000000000000000000000000000000000000000000", "000100000000000000000000000000000000000000000000000000000000000000000000000", "000000000010000000000000000000000000000000000000000000000000000000000000000", 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"000000000000000000000000000000000000000000000000000000000000000000000100000", "000000000000000000000000000000000000000000000000000000000000000000000001000", "000000000000000000000000000000000000000000000000000000000000000000000000100", "000000000000000000000000000000000000000000000000000000000000000000000000010", "000000000000000000000000000000000000000001000000000000000000000000000000000", "043201614564150602156165563244606233012336625111430545511012065512540415113", "000000000000000000000000000000000000000000100000000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000010000000000", "000000000000000000000000000000000000000000000000000010000000000000000000000", "000000000000000000000000000000000000000000001000000000000000000000000000000", "340504220643152126125651451601543545361632166426211231233361525300321261345", "032466044060345111405646320204646412200210124535360236523552514646515203066", "000000000000000000000000000000000000000000000010000000000000000000000000000", "000000000000000000000000000000000000000000000000000000000000000000000010000", "000000000000000000000000000000000000000000000000000000001000000000000000000", "000000000000000000000000000000000000000000000000100000000000000000000000000", "630520645112120566431622316363525034533105060154632345206560222621336451053", "242234536426503360562254444663352621143000656641310603632054160015432324666", "355444250106634031544435030233052450105405202525112601340463443516010553355"]); G:=MatrixGroup<75,F|x,y>; print "Group G is J1 < GL(75,GF(7))";