/* www-ATLAS of Group Representations. 6.M22 represented as 66 x 66 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,66,\[ 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, 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, 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 21,11,10,9,3,5,6,14,13,8,1,8,2,5,18,2,12,23,9,17,10,14,18,23,22,13,8,22,3,12,20,1,8,11,21,23,9,11,24,20,17,3,17,18,3,19,13,23,21,0,11,8,5,5,1,19,0,20,23,7,1,22,23,23,8,23, 15,8,1,23,23,5,3,21,0,10,16,15,22,3,14,17,2,22,15,2,7,20,23,12,12,5,22,5,8,5,12,23,19,2,22,6,19,20,14,16,21,3,16,12,23,9,19,3,23,16,20,9,1,22,0,21,4,8,18,24,0,4,3,3,4,15, 6,17,7,11,13,7,1,4,11,24,19,20,7,15,2,12,4,1,19,20,21,16,13,4,23,4,0,2,2,1,22,23,22,23,0,18,11,9,11,19,6,14,24,0,2,21,17,18,2,17,18,18,4,15,24,15,15,21,20,9,11,20,24,23,12,5, 13,15,20,8,0,16,14,1,11,19,24,6,14,17,13,16,2,14,22,24,3,21,8,7,9,24,8,23,15,14,7,12,16,7,1,22,3,17,10,1,13,16,12,10,0,13,11,13,1,13,19,12,2,12,13,17,15,14,24,14,16,2,2,0,8,21, 19,24,5,7,8,18,21,6,11,7,0,19,3,17,2,18,8,21,23,4,3,23,20,19,21,2,9,14,10,17,10,14,24,3,8,5,18,10,11,15,3,20,23,14,0,10,14,11,5,18,16,1,20,18,0,3,4,3,8,5,11,19,10,10,11,16, 1,11,18,3,24,0,12,2,21,1,5,13,6,23,13,16,17,10,20,11,0,0,5,2,4,16,13,2,3,7,10,23,4,18,20,17,6,11,16,22,19,11,23,23,15,20,4,7,22,4,17,18,2,12,14,18,8,21,23,10,22,5,5,19,19,9, 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, 1,19,0,0,23,9,10,23,20,16,3,1,11,23,15,21,18,19,10,17,3,23,2,3,21,6,12,5,12,13,12,20,10,6,10,15,7,4,2,20,22,2,22,11,21,22,3,22,13,12,17,19,3,2,8,13,10,2,10,4,4,6,20,6,6,21, 0,3,6,8,16,8,13,18,4,7,3,12,5,17,5,19,12,22,5,19,5,24,15,23,11,22,14,23,19,22,22,18,24,21,1,19,5,4,19,6,22,5,14,24,17,15,19,24,17,23,3,13,2,9,20,20,7,1,12,24,2,1,18,16,4,6, 1,5,12,22,17,12,12,6,7,11,15,24,5,24,0,5,7,17,8,6,17,4,3,9,1,24,1,0,18,19,20,1,14,12,21,24,20,9,4,20,6,13,13,22,0,17,16,7,5,22,0,3,11,12,11,6,0,2,21,20,15,23,14,13,24,8, 23,18,9,21,0,23,4,15,8,14,5,23,0,21,9,11,12,22,10,19,9,4,10,11,2,15,1,4,24,20,1,18,21,5,4,3,15,21,5,10,12,19,21,0,2,19,7,19,13,14,14,24,12,0,6,6,15,11,13,5,4,4,2,10,12,11, 14,8,22,19,19,16,3,5,4,17,14,18,21,7,11,15,17,8,0,12,23,8,15,17,22,15,4,17,0,7,22,6,15,22,24,0,14,21,24,0,12,16,9,14,7,13,9,20,19,12,18,10,22,23,23,3,14,11,24,2,6,9,18,17,10,7, 3,15,2,7,21,9,12,16,6,1,0,4,1,20,18,1,19,19,19,5,14,13,7,10,15,20,11,17,4,17,7,10,23,9,24,7,22,5,10,13,1,18,16,24,9,17,11,24,22,17,13,15,22,15,2,5,14,11,15,10,5,3,10,20,20,24, 9,14,23,0,21,7,0,24,17,22,17,18,2,0,18,14,3,14,12,18,20,9,8,23,18,3,20,1,8,0,12,6,19,7,22,18,23,11,11,15,5,13,21,24,2,16,16,10,20,21,7,8,16,20,17,11,22,23,4,10,8,3,3,7,3,5, 11,11,11,10,8,2,6,15,13,11,22,16,21,1,16,21,17,4,0,7,19,21,5,18,13,14,12,6,19,13,20,21,16,15,16,6,22,12,16,0,20,19,9,10,2,12,15,4,20,21,10,3,24,24,5,18,3,7,19,14,7,5,5,4,14,15, 20,1,8,2,0,1,2,22,0,15,11,16,20,4,2,6,21,10,1,2,22,11,7,10,14,2,2,14,24,11,1,22,16,24,6,14,6,5,0,13,6,14,21,16,8,6,9,17,16,5,6,22,14,22,0,6,24,18,13,21,13,6,13,17,7,5, 24,5,18,14,24,18,11,6,11,15,16,22,9,19,2,1,11,16,6,10,11,4,15,7,12,12,3,15,1,1,14,12,18,23,7,10,17,22,7,10,9,7,11,12,13,0,21,7,21,22,0,14,6,7,9,23,19,7,24,3,5,22,1,20,6,13, 22,4,19,2,14,19,13,9,23,10,11,16,22,4,9,16,15,14,0,15,13,16,11,16,22,23,22,4,0,6,16,12,15,17,11,3,9,17,1,23,5,13,4,4,2,6,8,24,23,16,4,1,21,18,17,6,7,13,6,19,9,8,1,12,13,14, 17,2,16,9,1,5,22,2,14,15,1,16,1,14,22,21,23,15,14,7,22,16,3,5,6,15,20,11,10,4,20,9,10,9,7,13,14,13,23,14,14,3,10,1,12,9,4,17,15,22,21,15,24,6,2,5,18,13,7,4,14,6,17,0,7,16]); G:=MatrixGroup<66,F|x,y>; print "Group G is 6.M22 < GL(66,GF(25))";