/* www-ATLAS of Group Representations. Sz(8) represented as 65 x 65 matrices over GF(125). */ F:=GF(125); x:=CambridgeMatrix(3,F,65,\[ 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, 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, 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 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, 0,61,49,89,2,34,114,115,11,41,97,1,93,77,34,63,38,7,29,56,84,55,89,67,75,47,45,114,84,61,94,27,75,112,102,69,36,86,94,26,50,116,4,87,30,53,22,53,72,83,0,111,69,58,124,23,120,22,116,13,80,87,10,75,55, 88,39,110,15,45,69,82,4,7,52,20,80,59,77,13,73,10,27,115,17,94,49,89,53,29,101,49,36,80,72,75,21,50,46,2,70,113,17,56,101,87,5,33,40,57,84,42,52,46,101,60,63,100,105,80,22,0,98,120,43,89,98,113,111,70, 63,65,1,24,76,63,29,120,92,107,89,62,27,82,42,120,10,81,73,51,118,18,86,79,47,92,94,56,91,115,53,73,122,120,9,2,62,116,19,53,42,79,87,85,25,74,31,99,12,63,29,99,22,41,121,71,53,97,54,109,25,44,32,120,26, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 104,64,116,23,94,29,97,63,66,118,61,88,90,112,92,51,5,105,122,4,10,57,77,77,80,7,114,122,96,41,29,61,68,113,61,94,77,65,25,74,78,5,55,103,117,7,105,15,35,69,117,0,2,74,77,16,0,30,40,86,26,75,45,11,82, 105,27,0,106,0,0,105,0,0,0,7,0,0,0,0,0,0,49,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 6,97,123,32,67,34,94,57,116,91,61,60,114,100,98,64,100,123,21,117,5,71,118,93,52,120,122,74,72,73,72,3,99,18,13,105,80,38,0,86,60,25,89,64,104,85,82,100,92,92,52,91,36,0,91,117,67,4,90,115,33,13,66,20,96, 101,10,88,21,6,9,28,80,34,81,40,39,12,8,44,72,64,113,48,114,100,94,29,82,120,48,88,71,27,29,22,36,79,33,21,75,34,34,116,24,59,90,62,6,107,31,70,58,20,3,3,88,100,3,52,65,14,98,12,8,113,109,38,115,28, 15,5,59,50,20,44,88,41,43,74,81,9,87,99,35,65,85,37,63,87,18,123,124,88,63,90,103,119,108,95,34,19,73,79,55,23,64,50,62,102,50,27,101,52,31,71,17,65,91,71,54,9,76,38,113,28,4,72,37,82,51,71,99,49,45, 2,16,12,5,34,43,42,116,110,1,112,96,83,26,86,85,34,29,111,29,62,1,83,37,3,50,65,43,90,47,81,88,79,14,2,37,92,45,84,95,91,62,102,113,46,105,110,88,14,23,14,35,120,33,32,41,75,53,55,28,66,11,35,60,19, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 118,69,82,107,118,43,29,118,59,23,67,2,16,61,40,69,37,67,123,32,83,27,98,7,118,113,2,88,41,54,38,16,79,65,12,15,29,75,29,110,32,20,5,63,79,107,47,47,103,81,3,118,4,17,45,31,6,24,88,116,96,105,105,116,52, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 62,3,53,8,0,124,46,64,39,13,95,121,6,106,79,95,112,63,124,69,52,110,103,13,51,123,72,83,120,106,98,63,123,99,32,81,43,109,121,50,93,80,33,95,21,21,94,14,10,116,54,114,15,124,50,121,95,82,34,90,99,122,37,86,47, 39,74,66,61,34,58,93,124,72,120,79,14,108,83,81,16,48,103,106,25,71,2,73,74,13,80,84,114,98,16,120,68,69,20,92,58,18,100,116,53,97,42,114,102,55,27,85,115,52,27,108,55,90,112,57,92,67,67,64,56,45,111,75,9,38]); G:=MatrixGroup<65,F|x,y>; print "Group G is Sz(8) < GL(65,GF(125))";