/* www-ATLAS of Group Representations. Fi22:2 represented as 78 x 78 matrices over GF(13). */ F:=GF(13); x:=CambridgeMatrix(3,F,78,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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9,9,11,11,10,6,10,2,6,4,4,2,0,7,4,11,4,8,9,0,5,7,9,6,11,2,1,8,11,9,2,4,5,3,7,9,0,6,0,0,2,12,1,0,0,11,0,0,2,0,4,0,0,3,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 5,5,4,4,7,1,7,7,1,11,6,7,5,3,11,2,6,3,7,5,1,3,6,1,2,10,11,3,3,7,8,2,1,0,5,6,0,1,0,0,10,0,11,12,0,3,0,0,8,0,2,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4,4,6,6,0,5,0,1,5,12,3,1,7,6,12,12,3,11,9,7,1,6,10,3,12,2,5,11,7,9,5,0,1,12,0,10,0,3,0,0,2,0,5,0,12,7,0,0,5,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8,8,11,11,11,6,11,5,6,0,8,5,4,0,0,12,8,8,3,4,12,0,5,4,12,5,8,8,3,3,10,11,12,0,9,5,0,4,0,0,5,0,8,0,0,3,12,0,10,0,11,0,0,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,8,8,0,0,0,4,0,12,9,4,4,0,12,0,9,0,6,4,5,0,5,3,0,4,12,0,8,6,5,4,5,12,10,5,0,3,0,0,4,0,12,0,0,8,0,12,5,0,4,0,0,12,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,2,10,10,11,0,11,5,0,6,11,5,4,6,6,10,11,12,0,4,3,6,1,12,10,6,9,12,1,0,1,1,3,4,5,1,0,12,0,0,6,0,9,0,0,1,0,0,1,12,1,0,0,4,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,2,3,3,0,2,0,2,2,0,6,2,11,7,0,1,6,11,7,11,10,7,9,2,1,2,3,11,8,7,5,12,10,1,9,9,0,2,0,0,2,0,3,0,0,8,0,0,5,0,12,12,0,1,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,12,12,0,12,0,0,12,0,1,0,0,0,0,0,1,0,12,0,0,0,0,0,0,0,0,0,0,12,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9,9,9,9,3,0,3,6,0,10,8,6,10,1,10,1,8,0,11,10,8,1,10,7,1,8,10,0,3,11,10,10,8,12,6,10,0,7,0,0,8,0,10,0,0,3,0,0,10,0,10,0,0,12,12,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12,12,5,5,10,8,10,1,8,6,6,1,5,5,6,12,6,3,1,5,12,5,2,2,12,0,12,3,9,1,5,11,12,4,9,2,0,2,0,0,0,0,12,0,0,9,0,0,5,0,11,0,0,4,0,9,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4,4,12,12,11,1,11,3,1,11,12,3,9,12,11,1,12,10,9,9,0,12,12,9,1,1,12,10,5,9,8,1,0,11,2,12,0,9,0,0,1,0,12,0,0,5,0,0,8,0,1,0,0,11,0,2,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,3,3,5,6,5,0,6,0,2,0,10,4,0,2,2,8,11,10,11,4,8,6,2,2,3,8,7,11,6,11,11,1,10,8,0,6,0,0,2,0,3,0,0,7,0,0,6,0,11,0,0,1,0,10,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 3,3,11,11,0,3,0,1,3,10,11,1,8,12,10,0,11,10,10,8,1,12,12,10,0,1,12,10,5,10,8,2,1,10,3,12,0,10,0,0,1,0,12,0,0,5,0,0,8,0,2,0,0,10,0,3,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12,12,8,8,5,4,5,7,4,2,3,7,3,7,2,3,3,8,2,3,12,7,12,9,3,7,11,8,2,2,10,1,12,3,1,12,0,9,0,0,7,0,11,0,0,2,0,0,10,0,1,0,0,3,0,1,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 6,6,6,6,6,0,6,9,0,0,7,9,5,4,0,2,7,1,7,5,0,4,4,1,2,11,9,1,4,7,8,0,0,1,2,4,0,1,0,0,11,0,9,0,0,4,0,0,8,0,0,0,0,1,0,2,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11,11,2,2,7,7,7,10,7,6,12,10,8,11,6,2,12,7,4,8,2,11,0,10,2,0,8,7,2,4,11,2,2,7,7,0,0,10,0,0,0,0,8,0,0,2,0,0,11,0,2,0,0,7,0,7,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9,9,6,6,11,6,11,4,6,10,0,4,2,4,10,12,0,7,6,2,1,4,7,12,12,3,3,7,0,6,0,0,1,9,0,7,0,12,0,0,3,0,3,0,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9,9,8,8,0,8,0,12,8,2,11,12,6,8,2,1,11,2,4,6,12,8,4,11,1,11,8,2,6,4,8,0,12,1,1,4,0,11,0,0,11,0,8,0,0,6,0,0,8,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,6,6,2,2,2,0,2,3,4,0,0,7,3,0,4,12,0,0,12,7,9,6,0,1,5,12,2,0,11,11,12,2,9,9,0,6,0,0,1,0,5,0,0,2,0,0,11,0,11,0,0,2,0,9,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,0, 5,5,0,0,10,1,10,8,1,1,3,8,0,10,1,12,3,10,12,0,2,10,0,3,12,6,1,10,3,12,10,3,2,0,6,0,0,3,0,0,6,0,1,0,0,3,0,0,10,0,3,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0, 10,10,4,4,3,0,3,11,0,10,6,11,0,3,10,1,6,11,4,0,0,3,1,10,1,12,8,11,10,4,3,1,0,10,3,1,0,10,0,0,12,0,8,0,0,10,0,0,3,0,1,0,0,10,0,3,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0, 9,9,4,4,11,6,11,5,6,10,1,5,2,5,10,12,1,7,5,2,1,5,6,11,12,3,3,7,0,5,12,1,1,9,0,6,0,11,0,0,3,0,3,0,0,0,0,0,12,0,1,0,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0, 11,11,1,1,9,9,9,4,9,2,5,4,2,12,2,3,5,9,2,2,1,12,12,3,3,7,7,9,3,2,8,2,1,4,4,12,0,3,0,0,7,0,7,0,0,3,0,0,8,0,2,0,0,4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0, 11,11,3,3,2,2,2,10,2,6,5,10,0,4,6,2,5,3,3,0,3,4,4,8,2,11,10,3,9,3,2,4,3,9,6,4,0,8,0,0,11,0,10,0,0,9,0,0,2,0,4,0,0,9,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0, 11,11,1,1,9,6,9,4,6,12,6,4,0,0,12,9,6,7,3,0,3,0,5,2,9,4,11,7,3,3,11,0,3,10,1,5,0,2,0,0,4,0,11,0,0,3,0,0,11,0,0,0,0,10,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0, 0,0,8,8,0,1,0,4,1,12,9,4,4,1,12,0,9,0,6,4,5,1,5,3,0,4,11,0,8,6,5,4,5,12,10,5,0,3,0,0,4,0,11,0,0,8,0,0,5,0,4,0,0,12,0,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,3,0,0,0,0,2,11,2,3,9,4,7,10,1,0,2,8,8,4,3,8,8,9,0,4,0,11,6,5,12,1,5,7,0,1,2,9,6,11,6,12,3,2,9,10,6,9,3,7,3,8,6,1,0,6,12,2,0,6,0,0,12,0,2,0,0,6,0,0,7,0,8,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 4,5,12,12,3,0,2,8,11,12,8,9,7,12,10,1,6,3,6,10,12,12,6,3,1,2,7,3,0,4,12,6,9,6,3,12,3,10,6,12,10,2,12,7,5,3,5,10,3,7,10,11,4,9,6,11,5,6,8,5,6,11,9,3,6,8,0,6,7,11,10,2,12,0,0,7,6,8, 9,5,1,12,0,7,9,1,1,11,3,5,7,0,0,6,4,12,3,0,7,7,4,11,10,8,7,11,7,6,12,11,12,12,5,8,6,0,1,12,8,6,5,5,11,12,10,5,1,5,8,7,4,11,7,4,4,3,11,6,6,4,8,9,10,3,7,0,10,8,9,0,1,9,1,12,7,0, 11,12,10,0,5,7,1,6,0,12,2,11,3,2,3,10,7,11,11,0,3,8,2,12,5,10,11,4,1,7,4,6,10,4,10,4,6,0,12,11,6,5,12,1,12,8,5,11,1,12,3,7,2,0,8,6,6,6,8,7,9,5,5,2,2,0,4,3,11,12,9,8,9,9,8,11,9,12, 3,11,9,6,9,8,6,0,12,3,2,5,10,6,4,0,8,3,3,0,2,10,12,4,8,12,1,8,1,4,2,2,4,3,3,8,1,5,7,4,5,8,2,2,10,7,6,1,4,4,3,9,4,12,7,3,9,8,8,0,0,8,5,7,7,9,4,6,2,10,9,0,4,1,12,5,1,7, 12,1,8,0,11,6,5,3,12,7,8,4,11,1,3,1,12,5,11,5,4,2,8,7,3,0,9,6,0,2,7,11,10,2,3,0,12,10,10,8,9,6,11,2,8,6,6,5,4,5,1,7,7,2,1,2,11,6,1,5,3,10,4,7,8,4,10,0,6,11,4,6,10,6,0,0,1,5, 6,2,3,10,0,12,9,10,8,1,0,4,0,5,5,1,1,7,4,10,0,3,4,8,1,8,8,12,2,1,3,10,0,5,9,12,1,10,1,10,5,8,9,10,4,9,6,4,6,5,3,6,0,8,10,1,6,12,10,1,9,0,3,2,6,1,9,3,8,6,2,1,7,11,7,7,2,7, 1,7,9,8,7,12,11,3,9,3,0,9,0,8,3,9,4,10,2,10,6,7,3,0,4,10,10,8,4,11,12,1,2,12,5,11,2,4,3,8,3,11,7,3,10,8,4,6,0,9,5,5,9,3,5,4,9,3,2,12,11,4,2,11,3,3,8,1,3,3,10,2,11,2,8,2,11,9, 4,8,2,0,4,6,9,5,1,6,0,4,12,7,3,2,12,11,4,4,9,2,8,12,4,0,8,6,1,9,0,10,6,5,4,6,10,4,6,8,12,10,10,9,9,12,8,5,10,2,7,10,10,3,9,11,1,0,4,1,6,12,0,12,3,8,7,1,9,7,0,1,9,12,12,9,9,12, 9,9,12,7,5,9,7,4,8,0,3,8,4,4,9,0,3,1,2,0,2,1,8,4,11,1,10,12,9,7,4,0,2,6,10,7,5,7,11,12,10,7,11,8,11,5,5,2,6,3,5,10,4,5,9,12,12,12,12,1,3,3,5,12,12,3,0,6,10,11,8,9,0,7,2,7,5,5, 6,5,9,6,3,8,9,9,8,1,8,11,2,6,12,2,4,12,2,1,1,6,11,10,1,11,2,0,12,1,8,5,4,3,1,7,5,12,0,1,11,2,2,10,9,8,0,5,11,10,2,8,6,12,0,0,11,6,10,9,6,6,6,0,2,4,5,12,0,5,4,7,6,4,5,6,8,2, 9,9,6,7,12,2,7,12,11,11,12,0,11,2,0,3,2,8,9,12,3,1,10,10,12,7,3,1,1,4,6,0,12,9,6,4,5,1,10,6,8,2,6,9,10,11,3,9,9,11,2,5,0,1,10,0,7,3,4,12,7,4,6,10,12,5,0,2,5,3,7,11,3,0,0,9,7,5, 11,3,7,11,6,1,0,4,3,4,12,10,10,5,11,2,12,2,10,10,0,5,3,2,8,10,0,4,2,3,4,8,11,4,2,7,7,8,0,7,4,5,5,4,3,6,8,9,12,4,4,0,10,3,6,4,6,5,9,9,8,9,9,11,0,8,4,7,4,10,6,11,3,10,9,0,3,2, 9,10,3,4,4,2,6,0,1,4,9,9,10,2,11,9,10,11,5,9,6,6,7,9,12,6,3,2,0,10,11,4,4,10,10,8,1,2,3,5,6,3,2,11,5,12,7,0,5,3,2,9,8,6,4,6,4,12,12,1,11,9,8,12,2,6,10,2,7,4,12,3,11,11,4,3,10,4, 8,12,2,11,10,6,1,9,7,8,5,2,11,6,2,9,10,7,3,1,0,1,5,10,11,10,7,0,12,6,2,8,11,1,4,8,1,10,6,4,1,11,11,10,1,7,4,7,1,1,11,8,7,12,9,2,0,5,3,12,12,1,11,7,2,6,5,11,7,9,6,0,5,10,0,5,8,2, 10,6,9,11,7,5,1,12,2,0,5,7,10,3,0,11,1,5,5,11,6,12,8,12,1,5,10,5,5,2,6,10,10,12,3,11,11,12,7,2,5,2,11,12,2,2,8,9,6,0,5,3,5,10,10,2,9,4,12,2,7,9,9,8,3,1,2,6,0,6,11,3,8,11,9,8,11,5, 12,0,11,6,11,12,9,5,2,3,4,2,6,1,1,8,5,1,4,3,7,4,4,10,9,8,3,0,5,8,8,12,12,4,3,0,6,6,4,11,8,12,7,12,9,12,8,12,12,0,0,9,7,11,1,1,9,0,4,9,5,11,10,1,6,0,1,8,12,2,9,4,12,10,10,3,11,6, 12,7,4,7,11,10,6,1,3,4,10,12,7,9,1,9,8,9,6,11,1,3,9,10,7,12,10,7,5,4,5,10,7,6,12,0,3,4,6,2,7,1,1,4,6,2,1,5,10,8,12,12,0,1,2,7,9,6,2,0,9,9,0,11,4,2,0,2,3,7,12,10,11,5,11,5,2,2, 5,0,7,1,8,8,5,6,10,7,6,5,11,8,2,5,7,12,6,4,7,3,12,11,8,11,9,10,4,1,12,10,1,4,0,8,3,7,3,7,9,3,8,4,12,4,5,2,9,8,5,9,2,2,7,10,10,8,2,9,1,7,7,10,5,2,1,10,8,5,4,10,12,0,9,3,1,2, 9,6,7,0,8,10,10,9,7,1,2,5,0,1,7,7,5,3,7,12,3,0,8,4,1,8,9,9,6,5,2,5,2,11,11,1,3,0,6,4,3,9,2,2,1,6,11,6,3,8,11,6,11,3,2,1,4,10,5,6,7,8,7,3,5,10,5,0,3,7,7,6,0,8,11,6,8,12, 6,4,0,9,10,8,5,12,7,3,1,12,0,6,9,9,0,5,4,10,9,0,2,7,8,6,0,8,6,4,4,2,5,11,7,11,11,2,12,1,12,1,10,5,10,4,7,2,3,4,7,9,2,5,9,12,0,7,7,10,12,0,5,6,9,11,2,8,2,3,12,7,1,3,7,5,7,9, 1,6,2,5,5,6,10,10,5,8,1,5,8,9,5,9,1,2,9,5,6,4,0,11,0,5,6,5,9,0,5,10,3,4,4,9,1,4,11,4,2,7,7,10,2,2,9,5,7,1,0,3,10,11,11,7,6,11,2,6,6,4,9,4,2,8,10,4,6,3,0,12,12,5,3,3,12,9]); G:=MatrixGroup<78,F|x,y>; print "Group G is Fi22:2 < GL(78,GF(13))";