/*
www-ATLAS of Group Representations.
M12 represented as 45 x 45 matrices over GF(5).
*/

F:=GF(5);

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",
"000000000000000000000000000000000010000000000",
"000000000000000000000000000000000001000000000",
"000000000000000000000100000000000000000000000",
"000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000001000",
"000000000000000000000000100000000000000000000",
"421300220240420244212242111220031432000003300",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000100000000000000000",
"030200003000000000004000000000000000040000000",
"302000300000000400000000000000000000400000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000100000000000000",
"103422413133033003032230331220203012320240000",
"000000000000000000000000000000010000000000000",
"411400401040010000000000001000000040000000100",
"314111200011041401304313000332000023002000340",
"133100244401311133334133134313431033233403104"]);

y:=CambridgeMatrix(1,F,45,[
"001000000000000000000000000000000000000000000",
"044000000000000000000000000000000000000000000",
"121000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000000100000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000001000000000000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000000000000000100000000000000000000000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000100000000000000000000000000",
"000000000000000000010000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000000000000000100000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000000000000000000000100000000000000000000",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000100000000000000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000100000000000000",
"000000000000000000000000000000010000000000000",
"000000000000010000000000000000000000000000000",
"000000000000000000000000000000000100000000000",
"000000000000001000000000000000000000000000000",
"000000000000000000000000000000000000100000000",
"000000000000000000000000000000000000010000000",
"000000000000000010000000000000000000000000000",
"000000000000000000000000000000000000000010000",
"000000000000000000000000000000000000000000100",
"000000000000000000000000000000000000000000010",
"000000000000000000000000000000000000000000001",
"344004341403220432133044401313041104340334310",
"143331120420023104032311301044400130002113410",
"000000000000000000001000000000000000000000000",
"410303331144100332121130424022244342011334143",
"232310411020014213011033134030322344321314100",
"431141421204241113010223323024233031001213022",
"000000000000000000000010000000000000000000000",
"343014404421411314232242123003210241034300410",
"000000000000000000000001000000000000000000000",
"422314433413231202311444122322004244030334242",
"000000000000000000000000010000000000000000000"]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is M12 < GL(45,GF(5))";