/*
www-ATLAS of Group Representations.
3.E6(4) represented as 27 x 27 matrices over GF(4).
*/

F<w>:=GF(4);

x:=CambridgeMatrix(1,F,27,[
"010000000000000000000000000",
"000100000000000000000000000",
"000010000000000000000000000",
"000000100000000000000000000",
"000000001000000000000000000",
"000000000010000000000000000",
"000000000000100000000000000",
"000000000000001000000000000",
"000000000000000010000000000",
"000000000000000000100000000",
"000000000000000000001000000",
"000000000000000000000010000",
"000000000000000000000000100",
"332222020331111112121212000",
"130113033123202102103000100",
"202110121231203211113023020",
"011103022220220002230203333",
"023210133032011221020020100",
"120331201102231333213322032",
"100101333311210300001322132",
"101023200003123131122020130",
"300203000023020310021101211",
"312131133223301032232313222",
"131310233320023100233323103",
"001030101103233001013211323",
"310231230313220211320230101",
"203312221311101210200132233"]);

y:=CambridgeMatrix(1,F,27,[
"001000000000000000000000000",
"011000000000000000000000000",
"000001000000000000000000000",
"000000010000000000000000000",
"000000000100000000000000000",
"000000000001000000000000000",
"000000000000010000000000000",
"000000000000000100000000000",
"000000000000000001000000000",
"000000000000000000010000000",
"000000000000000000000100000",
"000000000000000000000001000",
"000000000000000000000000010",
"000000000000000000000000001",
"120011023221301332012123233",
"223013113313331103011330133",
"113200122112032301333132113",
"233310232312232013320332113",
"331012231210003322102321100",
"023023011202311121102310121",
"231320200233213033333130031",
"210323320013323300021013010",
"330133322123003303031123200",
"131200100110321100003100113",
"111123122210013032133023120",
"330210230023023311201032121",
"203002130233131210112330302"]);

G<x,y>:=MatrixGroup<27,F|x,y>;
print "Group G is 3.E6(4) < GL(27,GF(4))";