/* www-ATLAS of Group Representations. 4.M22 represented as 56 x 56 matrices over GF(25). */ F:=GF(25); x:=CambridgeMatrix(3,F,56,\[ 0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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14,18,17,2,10,24,9,10,21,20,22,13,22,5,23,15,1,6,10,7,4,19,11,8,16,11,6,6,18,15,3,14,0,6,19,12,16,21,6,24,12,7,15,13,19,8,8,0,17,10,13,15,16,19,19,22, 10,3,21,17,2,4,17,8,11,23,10,6,21,0,17,5,10,17,15,23,6,8,24,21,23,6,8,18,13,2,10,13,23,23,14,9,23,5,17,9,9,23,18,23,13,6,19,3,7,13,1,20,17,19,12,6, 24,21,13,21,6,9,12,8,8,19,4,24,24,23,12,20,15,22,2,24,24,10,6,2,6,19,21,1,23,1,13,16,2,22,16,12,14,21,12,12,5,6,2,7,1,9,12,14,10,0,3,19,4,12,21,2, 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, 8,7,15,22,10,12,11,0,1,19,3,17,4,22,24,4,16,9,21,6,2,22,8,2,17,2,23,1,15,24,11,5,24,14,24,11,24,10,20,20,19,21,11,5,0,22,17,3,20,3,1,16,2,7,22,4, 8,20,21,19,18,15,1,17,22,8,17,15,8,14,10,18,8,24,2,18,17,19,11,2,18,16,16,5,22,20,3,10,8,4,11,1,16,0,10,2,13,2,21,3,16,0,13,14,20,4,14,17,12,9,19,2, 24,20,16,0,17,23,11,23,12,18,5,24,3,0,3,11,14,13,24,15,22,7,18,10,10,0,1,23,0,7,15,19,2,23,5,8,19,0,14,18,7,1,15,21,13,18,1,22,5,20,15,4,12,23,8,10, 13,24,22,16,17,0,7,21,3,11,18,16,15,2,18,12,22,16,24,4,10,18,10,1,22,21,1,3,24,20,6,4,2,2,2,20,16,11,12,24,3,20,5,12,22,5,19,19,15,4,9,2,12,12,4,6, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 18,11,9,10,2,6,8,15,15,13,7,11,6,15,13,12,9,0,8,11,18,20,10,5,2,6,2,14,16,2,14,3,16,23,14,22,23,20,14,24,21,20,0,0,8,17,22,24,3,2,3,2,7,0,10,16, 16,3,2,15,13,24,7,19,10,14,3,5,10,21,11,8,18,19,22,18,4,10,10,20,10,10,7,7,6,10,13,13,16,10,1,9,13,21,3,16,0,23,15,13,3,13,9,24,0,4,12,5,20,9,2,5, 16,20,16,12,14,1,14,18,10,23,5,12,17,8,11,1,13,1,14,15,2,14,8,17,3,13,18,2,3,19,17,8,7,0,24,13,21,16,0,16,19,16,19,14,12,8,12,9,24,10,23,12,5,5,16,19, 1,2,2,3,2,2,0,1,2,1,0,1,4,0,0,1,0,0,0,2,0,1,0,0,0,0,1,0,4,0,0,0,0,0,0,2,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]); G:=MatrixGroup<56,F|x,y>; print "Group G is 4.M22 < GL(56,GF(25))";