/*
www-ATLAS of Group Representations.
3.M22 represented as 45 x 45 matrices over GF(7).
*/

F:=GF(7);

x:=CambridgeMatrix(1,F,45,[
"010000000000000000000000000000000000000000000",
"100000000000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"001000000000000000000000000000000000000000000",
"000000100000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000000000001000000000000000000000000000000000",
"000000000000010000000000000000000000000000000",
"000000000000000100000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000000000000100000000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000000000000000001000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000000000000000001000000000000000000000",
"000000000000000000000000010000000000000000000",
"000000000000100000000000000000000000000000000",
"000000000000000000000000000100000000000000000",
"000000000000001000000000000000000000000000000",
"000000000000000000000000000000100000000000000",
"000000000000000000000000000000010000000000000",
"000000000000000010000000000000000000000000000",
"000000000000000000000000000000000010000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000000000000000000000100000000",
"000000000000000000010000000000000000000000000",
"000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000001000",
"000000000000000000000100000000000000000000000",
"000000000000000000000010000000000000000000000",
"340242460226561101013430232043146160216514500",
"421600224330040453606326222204516432614156336",
"000000000000000000000000100000000000000000000",
"655066312461242644461535155221141266661223335",
"000000000000000000000000001000000000000000000",
"060334145514463514212015105612260554145151251",
"441264021036416451610624356414264112131212443",
"000000000000000000000000000010000000000000000",
"004145143106552365104113633365536105445102655",
"000000000000000000000000000001000000000000000",
"453341225306054103435155562404354451560043111",
"010143326332565461655404043006145200116621304",
"624246360165253453205464664513152124221015343"]);

y:=CambridgeMatrix(1,F,45,[
"001000000000000000000000000000000000000000000",
"066000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"106010000000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000000000000001000000000000000000000000000000",
"000000000000000010000000000000000000000000000",
"000000000000000001000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000000000000000000010000000000000000000000000",
"000000000000000000000100000000000000000000000",
"000000000000000000000010000000000000000000000",
"000000000000000000000000100000000000000000000",
"000000100001006000000000000000000000000000000",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000010000000000000000",
"000000000000000000000000000001000000000000000",
"000000100000000000000000000000000000000000000",
"000000000000000000000000000000001000000000000",
"000000000000000000000000000000000100000000000",
"000000010000000000000000000000000000000000000",
"000000000000000000000000000000000001000000000",
"000000000000000000000000000000000000010000000",
"000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000010000",
"000000100001000000006000000000000000000000000",
"000000000000000000000000000000000000000000100",
"000000000000000000000000000000000000000000010",
"000000000000000000000000000000000000000000001",
"411442165524546466400314051100456603321563616",
"260521344143636251463343164241512536012052421",
"603560664330130622510160665036605024242452631",
"245306655366364245430222130555564615134353310",
"163545106130510402410430131231554561363535361",
"250356102624634132655056360656006121650055065",
"515654321545401243115646024510443541444141652",
"000000000000010000000000000000000000000000000",
"435041305341653651433646004321123150154230332",
"621605641442464632533620334441666325233620042",
"451231601152512406264253455253415344322334414",
"000000000000000100000000000000000000000000000"]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is 3.M22 < GL(45,GF(7))";