/*
www-ATLAS of Group Representations.
M12 represented as 45 x 45 matrices over GF(3).
*/

F:=GF(3);

x:=CambridgeMatrix(1,F,45,[
"010000000000000000000000000000000000000000000",
"100000000000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"001000000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000100000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000000000000010000000000000000000000000000000",
"000000000000001000000000000000000000000000000",
"000000000000000010000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000001000000000000000000000000000000000",
"000000000000000000001000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000000000000000000000010000000000000000000000",
"000000000000000000000001000000000000000000000",
"000000000000000000000000010000000000000000000",
"000000000000000100000000000000000000000000000",
"000000000000000000000000000010000000000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000100000000000000000000000000",
"000000000000000000000000000000001000000000000",
"000000000000000000010000000000000000000000000",
"220000202000000000000000002000000000000000000",
"000000000000000000000000000000000010000000000",
"000000000000000000000100000000000000000000000",
"000000000000000000000000000000000000100000000",
"000000000000000000000000000000000000010000000",
"111122020222222021110211210022222000220000000",
"000000000000000000000000100000000000000000000",
"000000000000000000000000000000000000000001000",
"000000000000000000000000000100000000000000000",
"000000020200000000000200000020000002000000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000100000000000000",
"000122112121010020100000000200202101222111212",
"010202010012011000112000122201002020100102201",
"101111022021011212220100201002012100120021200",
"000000000000000000000000000000000100000000000",
"211122100112002112222100201001112000000000100",
"121112001212111102110201212211212012110021110",
"022200022022012212120102201202112120100001202"]);

y:=CambridgeMatrix(1,F,45,[
"110000000000000000000000000000000000000000000",
"001000000000000000000000000000000000000000000",
"022000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000000100000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000001000000000000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000000000000000100000000000000000000000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000100000000000000000000000000",
"000000000000000000010000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000000000000000100000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000000000000000000000100000000000000000000",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000100000000000000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000100000000000000",
"000000000000000000000000000000010000000000000",
"000000000000010000000000000000000000000000000",
"000000000000000000000000000000000100000000000",
"000000000000001000000000000000000000000000000",
"000000000000000000000000000000000001000000000",
"022120000100200000002000000010000001000000000",
"000000000000000010000000000000000000000000000",
"000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000010000",
"000000000000000000000000000000000000000000100",
"000000000000000000000000000000000000000000010",
"000000000000000000001000000000000000000000000",
"000000000000000000000000000000000000000000001",
"010121200022002120000222012002020120201211210",
"000000000000000000000010000000000000000000000",
"000000000000000000000001000000000000000000000",
"010010102022010002110111221122122112212112012",
"220022110202120121221212202112221122120202011",
"000000000000000000000000010000000000000000000",
"012222221021010100101011110100110121001100120",
"121010210202020021120120212100110101022111110"]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is M12 < GL(45,GF(3))";