/* www-ATLAS of Group Representations. M23 represented as 231 x 231 matrices over GF(49). */ F:=GF(49); x:=CambridgeMatrix(3,F,231,\[ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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31,29,40,35,34,8,17,42,41,23,14,1,11,42,23,19,19,30,42,46,21,32,47,13,37,9,19,24,25,6,27,2,44,21,44,32,20,7,28,25,42,42,24,46,9,46,34,6,42,17,20,14,29,13,22,20,10,6,36,32,45,11,29,25,16,35,18,26,48,29,16,35,34,27,35,26,22,16,22,48,5,30,8,24,27,18,6,42,11,40,37,14,30,24,28,7,13,6,16,25,20,11,1,48,8,26,20,0,45,2,7,7,29,6,15,12,38,11,10,28,31,0,17,42,15,26,43,40,31,28,26,36,2,21,3,30,15,15,45,15,36,21,12,39,19,28,28,5,3,5,42,12,33,47,23,48,37,0,30,0,14,43,7,19,42,23,39,33,41,9,48,39,41,7,3,27,47,21,39,33,48,19,14,47,48,20,11,38,13,18,5,45,22,17,9,1,36,37,26,34,41,27,6,21,4,22,23,25,8,47,47,15,25,25,4,45,40,48,42,42,46,22,44,20,43,1,7,34,44,23,23, 11,20,38,13,32,39,44,25,36,30,44,6,7,26,14,46,27,30,27,17,7,38,38,14,35,40,40,43,39,15,43,6,46,5,42,18,39,20,39,25,0,12,3,34,44,31,31,45,45,12,37,21,7,40,18,38,43,5,21,32,42,39,8,26,7,48,7,18,17,18,41,19,11,8,32,48,6,4,30,43,43,16,24,34,47,41,46,11,47,12,23,45,28,47,24,20,39,48,36,6,8,21,32,17,35,46,13,46,48,18,19,3,25,43,19,7,45,19,46,31,11,47,36,38,10,40,38,26,12,12,31,19,38,0,23,25,13,33,3,39,34,10,12,38,26,37,6,48,20,19,10,11,13,7,19,45,16,29,42,0,43,27,10,38,2,20,16,2,32,27,47,44,13,44,12,5,28,25,5,9,7,3,12,4,0,27,46,23,10,23,12,41,16,6,32,20,48,18,34,30,12,39,14,19,47,12,23,39,19,37,46,2,4,0,1,48,25,2,43,35,18,16,46,15,24,24,22,2,9,46,41, 44,10,0,23,11,22,29,19,17,16,46,6,46,48,16,37,30,43,6,12,43,1,45,19,13,37,28,39,17,31,41,24,14,41,25,43,43,30,2,16,23,12,16,14,27,30,27,17,25,3,21,47,46,38,14,4,25,9,29,11,24,32,8,23,4,27,1,29,7,14,23,48,43,46,22,22,32,22,40,7,25,36,15,3,42,20,45,10,32,17,44,47,8,45,22,10,8,45,2,22,43,44,30,18,21,34,16,20,40,20,41,44,45,2,31,22,42,12,10,15,45,25,45,17,24,17,27,19,46,9,2,0,1,7,44,47,1,14,0,26,37,25,13,6,23,34,5,22,25,32,42,44,32,26,24,5,6,33,46,32,0,31,32,21,3,32,22,32,23,27,20,2,1,13,43,48,17,29,48,47,5,12,16,34,27,15,0,18,19,46,8,19,11,25,3,17,48,2,5,35,39,30,41,29,25,19,10,16,18,46,3,37,38,33,27,43,7,43,13,42,46,16,31,5,3,4,28,39,33,34,10, 26,29,4,35,1,1,0,15,18,43,32,14,13,34,47,15,45,32,4,6,26,15,41,29,20,2,31,24,24,46,15,1,7,46,1,2,29,46,6,1,11,23,25,39,27,38,15,16,4,10,33,47,19,21,4,0,35,48,8,4,34,19,1,3,25,35,31,8,33,18,29,30,10,31,22,26,16,44,8,6,11,4,18,36,10,13,7,35,1,24,47,37,36,15,14,42,4,21,9,12,17,45,17,43,19,10,27,7,2,37,30,4,32,43,22,21,23,20,32,12,28,20,31,23,16,34,13,47,17,0,39,9,37,17,41,7,25,42,13,12,16,10,18,5,7,39,7,17,30,22,47,2,39,37,16,42,31,3,39,20,23,20,29,35,11,22,20,38,26,15,36,34,44,38,47,21,46,16,34,20,38,1,42,12,6,13,34,35,9,34,38,37,24,38,17,45,1,45,18,32,47,37,31,21,4,27,42,4,8,41,27,12,30,34,43,36,48,14,42,20,42,25,41,8,18,37,12,9,46,34,17, 34,14,20,15,44,31,40,32,7,18,46,29,47,34,16,9,9,5,23,5,2,28,43,13,5,11,8,36,33,28,42,4,2,15,32,41,26,18,40,17,21,14,6,15,17,4,39,10,10,27,26,37,42,10,22,34,4,39,37,29,28,48,47,9,25,12,21,20,18,40,5,21,6,28,40,44,32,12,40,8,8,13,46,34,37,10,35,1,11,36,43,25,7,30,19,36,25,5,46,4,10,5,8,9,41,37,22,23,34,8,39,27,44,44,36,46,8,19,18,24,32,10,44,22,12,19,12,33,36,43,18,17,5,29,26,18,8,13,1,38,3,37,5,7,39,9,15,6,33,18,16,14,45,24,18,24,15,20,39,30,16,38,1,23,44,47,44,14,45,30,45,32,33,32,12,45,7,27,3,26,41,37,30,33,26,34,33,23,27,20,18,39,34,47,2,20,41,34,34,19,6,47,38,3,47,5,11,41,17,27,47,32,36,4,31,38,6,40,42,4,42,29,0,13,20,18,46,10,17,41,37, 14,24,21,9,45,30,16,29,24,30,1,26,13,5,24,3,38,43,46,21,22,11,23,44,46,21,30,45,5,28,24,19,10,37,45,29,30,7,10,31,5,30,1,21,42,45,21,14,18,2,14,40,22,45,37,31,3,11,27,31,44,21,43,20,19,45,6,10,15,30,38,38,12,43,19,3,11,3,41,48,16,0,13,10,0,0,37,39,12,25,42,29,48,0,11,30,33,30,12,6,0,42,3,34,39,35,45,5,8,45,36,45,4,14,37,31,11,30,29,28,24,26,42,6,13,24,21,3,38,21,38,26,3,25,1,28,10,32,47,34,22,40,34,26,12,12,38,27,22,39,47,3,48,2,13,36,22,43,34,34,26,13,27,42,25,32,37,37,22,37,17,43,32,21,10,10,17,2,39,19,32,37,12,25,47,26,35,28,17,28,40,48,42,31,40,31,28,21,1,23,27,43,42,21,34,35,30,41,16,6,38,19,0,34,43,13,21,38,12,25,34,12,32,5,41,7,23,25,27,3,27, 16,14,37,40,21,6,4,23,19,3,9,1,29,16,21,30,47,35,46,46,6,27,15,48,25,48,38,32,5,28,10,4,38,0,28,43,7,38,1,39,22,47,15,38,10,18,1,37,16,10,31,5,38,40,1,30,42,6,31,36,20,4,17,0,35,3,4,4,44,21,28,11,29,22,35,25,48,39,5,42,23,28,11,21,24,19,38,13,0,5,3,36,46,33,38,37,46,45,11,6,14,36,46,41,15,10,26,43,23,20,40,40,9,4,33,28,47,42,29,2,4,19,8,4,26,22,17,15,31,25,1,18,0,17,5,1,48,20,8,38,19,40,0,15,13,4,38,39,32,17,19,0,42,16,17,21,5,27,33,37,17,21,17,14,42,18,16,3,44,42,16,44,31,33,10,26,31,12,11,33,25,4,9,41,30,20,39,32,9,20,30,2,19,40,39,24,15,8,26,12,12,39,8,45,47,44,42,35,23,14,25,47,23,23,4,18,44,33,17,29,9,21,16,5,22,21,39,11,35,7,33, 7,34,2,32,3,13,23,5,7,33,0,8,46,26,4,11,1,17,5,21,5,0,13,33,6,44,8,22,16,20,35,47,31,13,22,33,34,2,25,37,27,11,45,42,4,43,41,4,5,0,1,22,26,44,28,13,3,36,43,44,8,8,18,28,41,32,30,1,14,22,2,30,37,27,21,12,28,23,30,0,12,10,26,38,33,37,21,17,29,36,45,8,23,47,41,23,10,30,18,32,7,12,28,12,37,23,18,20,14,2,43,13,35,12,32,32,36,15,8,12,12,47,20,34,26,41,20,26,40,12,9,4,41,17,33,3,21,20,34,33,34,22,5,37,39,48,32,5,40,33,47,6,20,22,27,17,37,34,32,7,6,22,31,28,1,6,29,35,24,16,21,44,5,30,26,34,30,0,16,29,14,44,37,9,23,16,35,40,48,8,21,11,1,16,3,16,43,25,33,41,16,17,38,19,17,35,30,34,12,33,30,46,30,24,45,31,6,21,26,2,34,45,9,1,10,39,31,30,3,11,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 42,4,7,32,21,2,7,13,17,40,5,36,14,1,3,47,48,10,6,40,38,26,9,11,29,24,7,18,27,25,3,45,11,13,46,48,29,41,3,28,7,24,25,15,7,10,7,21,28,34,45,39,46,26,23,27,22,32,39,8,1,31,15,35,7,41,21,15,16,8,42,10,35,47,24,17,28,19,35,35,42,32,45,1,32,15,32,15,16,26,20,6,45,4,47,3,32,25,14,8,42,5,14,10,13,42,22,17,32,11,7,16,43,2,34,13,27,40,38,15,16,33,20,4,12,35,2,5,14,1,8,31,19,24,8,20,48,8,27,3,32,3,33,43,26,24,33,23,2,33,40,28,24,4,21,39,33,0,33,4,5,10,34,35,21,4,23,7,46,29,37,24,11,47,19,10,36,6,39,1,14,43,9,3,0,36,41,12,6,32,27,28,16,24,36,45,35,18,15,42,23,35,38,2,27,6,46,19,43,21,6,46,28,21,27,13,35,2,5,7,33,25,47,19,48,4,37,38,11,38,42, 8,6,7,25,24,48,29,24,10,47,25,21,48,2,23,15,7,0,48,46,6,1,48,11,19,45,28,8,48,27,11,18,29,14,45,38,38,10,25,38,42,2,35,30,36,21,7,47,15,45,46,3,5,33,3,12,2,29,15,37,40,23,37,21,9,18,40,42,39,11,6,28,46,2,34,22,48,8,48,35,41,39,44,19,36,17,19,43,16,40,1,29,37,17,3,34,14,33,21,6,6,21,39,37,28,2,47,23,27,15,17,48,32,32,28,8,39,3,37,42,28,33,44,42,25,29,3,39,41,40,32,33,20,6,32,31,29,8,18,45,1,33,23,41,38,30,30,48,19,46,23,34,11,4,3,30,4,9,14,9,28,47,20,28,23,7,12,44,17,33,36,0,4,6,5,38,6,48,35,38,2,10,8,35,12,6,44,21,4,13,5,13,20,9,42,20,11,47,22,0,3,48,15,17,28,45,38,6,32,44,23,47,18,3,42,19,42,30,30,35,15,21,41,43,30,46,42,31,26,46,33, 32,32,17,0,15,13,39,20,5,21,15,19,13,43,26,23,44,27,27,11,40,14,35,33,46,25,3,16,39,24,11,41,30,21,8,6,38,37,14,1,41,28,10,11,48,0,25,8,0,12,25,42,23,38,6,10,35,15,38,38,27,25,45,12,2,25,17,8,14,36,8,0,8,48,9,13,29,5,47,3,46,13,23,32,29,36,16,25,29,46,36,5,9,7,19,41,38,30,40,18,47,34,14,45,44,28,32,15,21,18,17,19,32,5,45,4,26,10,41,16,45,10,37,24,36,1,30,44,31,4,17,4,9,11,10,7,40,17,21,29,5,9,21,35,43,4,42,1,33,47,23,45,24,45,17,31,26,21,43,22,42,7,45,1,21,15,19,24,33,3,20,11,4,14,33,10,6,35,8,41,12,47,35,24,17,31,40,2,28,44,42,37,40,13,27,6,20,44,38,28,42,6,30,0,31,44,33,27,14,17,27,8,39,38,26,28,16,26,14,25,22,1,4,42,48,19,39,21,45,36,39, 45,29,40,6,38,5,34,16,42,40,30,7,45,8,0,8,37,20,17,11,46,44,45,5,34,31,14,14,1,39,47,23,0,33,48,27,9,48,40,42,31,16,34,43,13,48,47,6,31,6,8,44,15,46,0,2,16,42,39,29,25,44,10,44,43,29,18,24,46,39,34,44,5,47,31,24,19,27,28,6,40,3,17,15,18,47,16,10,24,17,44,15,12,8,1,36,17,34,31,5,43,27,0,3,13,10,25,48,35,30,36,34,41,2,43,6,48,31,38,16,43,26,10,12,39,20,4,7,0,15,26,46,2,26,24,3,18,37,39,16,28,7,15,23,42,35,23,31,27,27,35,18,13,14,9,20,19,31,0,8,15,21,35,1,39,21,48,42,24,42,35,19,2,28,8,23,42,12,24,13,44,24,15,15,38,32,47,1,10,32,20,32,43,32,28,35,10,4,8,27,43,41,43,14,24,32,43,14,26,12,28,8,19,14,47,7,24,41,28,34,22,47,48,40,3,40,13,3,44,13,38, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 2,20,25,34,22,38,48,6,10,11,24,22,5,8,8,0,28,24,23,9,31,14,45,24,8,19,39,1,35,21,12,35,21,40,43,38,19,32,33,3,38,24,19,45,48,35,1,36,8,0,3,14,26,16,30,40,1,15,11,32,18,34,29,0,20,11,26,40,17,10,45,24,25,4,0,7,45,3,21,25,1,11,21,31,23,4,40,34,23,26,5,13,47,0,3,39,14,36,14,16,3,17,7,37,22,23,22,28,18,4,8,42,9,44,2,14,12,33,21,10,41,20,27,38,18,14,44,37,10,47,6,27,47,8,39,44,37,28,34,16,34,42,18,12,10,26,18,24,6,18,36,43,38,25,7,45,4,10,14,4,32,0,36,28,11,17,25,42,30,15,30,15,0,28,32,33,12,48,3,28,0,4,31,22,34,17,23,3,31,41,26,37,12,28,46,41,36,34,21,36,23,22,15,48,39,44,21,6,44,5,22,8,32,22,31,30,20,20,42,24,27,38,23,1,15,22,17,15,42,36,30, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]); G:=MatrixGroup<231,F|x,y>; print "Group G is M23 < GL(231,GF(49))";