/*
www-ATLAS of Group Representations.
3.Fi22 represented as 27 x 27 matrices over GF(4).
*/

F<w>:=GF(4);

x:=CambridgeMatrix(1,F,27,[
"010000000000000000000000000",
"100000000000000000000000000",
"000010000000000000000000000",
"000000100000000000000000000",
"001000000000000000000000000",
"000000000100000000000000000",
"000100000000000000000000000",
"000000000000100000000000000",
"000000000000001000000000000",
"000001000000000000000000000",
"000302321210201000000000000",
"113231233101303000000000000",
"000000010000000000000000000",
"000001022100212000000000000",
"000000001000000000000000000",
"330003033300303100000000000",
"222323330300300010000000000",
"331212202200002001000000000",
"330003033300303000100000000",
"330303320300200000010000000",
"001013032300302000001000000",
"221210203000003000000100000",
"330101110100100000000010000",
"332023021300201000000001000",
"000200200000000000000000100",
"111313310300100000000000010",
"000101131100301000000000001"]);

y:=CambridgeMatrix(1,F,27,[
"002000000000000000000000000",
"000200000000000000000000000",
"000002000000000000000000000",
"000000020000000000000000000",
"000000002000000000000000000",
"000000000020000000000000000",
"000000000002000000000000000",
"000000000000020000000000000",
"020022002000000000000000000",
"000000000000000200000000000",
"000000000000000020000000000",
"000000000000000002000000000",
"000000000000000000200000000",
"000000000000000000020000000",
"000000000000000000002000000",
"000000000000000000000200000",
"000000000000000000000020000",
"000000000000000000000002000",
"000000000000000000000000200",
"000000000000000000000000020",
"000000000000000000000000002",
"323131311210223023001331011",
"331200102100323023022031013",
"330023130313132330322223301",
"231301020300331101011311220",
"113200333010321301321313323",
"110302101330232220030003000"]);

G<x,y>:=MatrixGroup<27,F|x,y>;
print "Group G is 3.Fi22 < GL(27,GF(4))";