/*
www-ATLAS of Group Representations.
3.E6(4).2g represented as 54 x 54 matrices over GF(4).
*/

F<w>:=GF(4);

x:=CambridgeMatrix(1,F,54,[
"010000000000000000000000000000000000000000000000000000",
"100000000000000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000000000000",
"000000100000000000000000000000000000000000000000000000",
"001000000000000000000000000000000000000000000000000000",
"000000000100000000000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000000000000",
"000000000000100000000000000000000000000000000000000000",
"000000000000001000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000000000000",
"000000000000000010000000000000000000000000000000000000",
"000000000000000000100000000000000000000000000000000000",
"000000010000000000000000000000000000000000000000000000",
"000000000000000000000100000000000000000000000000000000",
"000000001000000000000000000000000000000000000000000000",
"000000000000000000000001000000000000000000000000000000",
"000000000010000000000000000000000000000000000000000000",
"000000000000000000000000001000000000000000000000000000",
"000000000001000000000000000000000000000000000000000000",
"000000000000000000000000000001000000000000000000000000",
"000000000000000000000000000000010000000000000000000000",
"000000000000010000000000000000000000000000000000000000",
"000000000000000000000000000000000010000000000000000000",
"000000000000000100000000000000000000000000000000000000",
"000000000000000000000000000000000000010000000000000000",
"000000000000000000000000000000000000000100000000000000",
"000000000000000001000000000000000000000000000000000000",
"000000000000000000000000000000000000000000100000000000",
"000000000000000000000000000000000000000000010000000000",
"000000000000000000010000000000000000000000000000000000",
"000000000000000000000000000000000000000000000010000000",
"000000000000000000001000000000000000000000000000000000",
"000000000000000000000000000000000000000000000000010000",
"003133132331302331101033301210310130030000210030000000",
"000000000000000000000010000000000000000000000000000000",
"112220200002020203220202013132201001000100130020010000",
"332020022022202221203022131330133020110300330010030000",
"000000000000000000000000100000000000000000000000000000",
"000201212103122200311202000231311000001000230030010000",
"000000000000000000000000010000000000000000000000000000",
"333131111122121321230213301133103010030010130010030000",
"332223200320020321000223101020003020010001020000030000",
"000000000000000000000000000100000000000000000000000000",
"000000000000000000000000000010000000000000000000000000",
"330302321212231211210302111121300000010100121030000000",
"333231221102211002213110012221333010000100220130030000",
"000000000000000000000000000000100000000000000000000000",
"222320310032100230212032110211321030010100210031010000",
"000302320230230030030300000013301000000000010030110000",
"000000000000000000000000000000001000000000000000000000",
"111110100022030023220310113332201010010100330020011000",
"110300333031323031133220231333032020020300330000020100",
"330102103221033123110311123021200010010200020020000010",
"111113120321210123100111123220300010010200220030000001"]);

y:=CambridgeMatrix(1,F,54,[
"001000000000000000000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000000000000",
"000000000010000000000000000000000000000000000000000000",
"000000000001000000000000000000000000000000000000000000",
"000000000000010000000000000000000000000000000000000000",
"011011001000000000000000000000000000000000000000000000",
"000000000000000100000000000000000000000000000000000000",
"000000000000000001000000000000000000000000000000000000",
"000000000000000000010000000000000000000000000000000000",
"000000000000000000001000000000000000000000000000000000",
"111100000010010001000000000000000000000000000000000000",
"000000000000000000000010000000000000000000000000000000",
"000000000000000000000000100000000000000000000000000000",
"000000000000000000000000010000000000000000000000000000",
"000000000000000000000000000100000000000000000000000000",
"000000000000000000000000000010000000000000000000000000",
"000000000000000000000000000000100000000000000000000000",
"000000000000000000000000000000001000000000000000000000",
"000000000000000000000000000000000100000000000000000000",
"000000000000000000000000000000000001000000000000000000",
"000000000000000000000000000000000000100000000000000000",
"000000000000000000000000000000000000001000000000000000",
"000000000000000000000000000000000000000010000000000000",
"000000000000000000000000000000000000000001000000000000",
"100000000000000000000000000000000000000000000000000000",
"000000000000000000000000000000000000000000001000000000",
"000000000000000000000000000000000000000000000100000000",
"000000000000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000000000000001000",
"000000000000000000000000000000000000000000000000000100",
"000000000000000000000000000000000000000000000000000010",
"000000000000000000000000000000000000000000000000000001",
"100221222123102033223033212211100230303203111003200122",
"202022201011112032233203130232311331120032101302222012",
"331230032123032332231223022001310310112301233331301331",
"330332223320303132023321321320011120111122011110012020",
"213121320132013230202311302202333033112301111113302220",
"113200311201322231321030012320212310030222130031220331",
"300121112033333201020230130331311022302222013300221210",
"112323011322232001332303020023210323320020121011311300",
"131313303232121022313123331103023322120103301122233210",
"233000022103133002002332110032121331300223010003313203",
"122222003110010000300130212001231031020121003002131103",
"333011110003123310123200311203312331202302210131212031",
"331033003133222023122323321133030320011201303023033222",
"110311223211013131022300302032330310303320110112323003",
"021113033330020313333033330232201223210300113212023121",
"102103102331201211123322322002233011110001131321310213",
"312032010012020203130313020130101300321010311132130010",
"330111310101112001131300000103130222121203011031223130"]);

G<x,y>:=MatrixGroup<54,F|x,y>;
print "Group G is 3.E6(4).2g < GL(54,GF(4))";