/*
www-ATLAS of Group Representations.
3.M22 represented as 45 x 45 matrices over GF(4).
*/

F<w>:=GF(4);

x:=CambridgeMatrix(1,F,45,[
"010000000000000000000000000000000000000000000",
"100000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000000100000000000000000000000000000000000000",
"001000000000000000000000000000000000000000000",
"000000000100000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000000000001000000000000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000000000000001000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000000000000100000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000000000000000100000000000000000000000",
"000000000000000000000001000000000000000000000",
"000000000000000000000000010000000000000000000",
"000000000000010000000000000000000000000000000",
"000000000000000000000000000010000000000000000",
"000000000000000000000000000000100000000000000",
"000000000000000100000000000000000000000000000",
"000000000000000000000000000000000100000000000",
"000000000000000010000000000000000000000000000",
"000000000000000000000000000000000001000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000010000",
"000000000000000000010000000000000000000000000",
"000000000000000000000000000000000000000000100",
"000000000000000000001000000000000000000000000",
"112303031020310011311203221230022110203213130",
"232230013202322010202330301013131112223311011",
"000000000000000000000010000000000000000000000",
"210212300222010212332000131321203313330132130",
"000000000000000000000000100000000000000000000",
"120200022103031133013103230211100100303203301",
"313021230323302210302030112211103200022213232",
"000000000000000000000000001000000000000000000",
"131002221002200032332232130221103200030313232",
"000000000000000000000000000100000000000000000",
"011201133021032221301213121312312221210123000",
"000000000000000000000000000001000000000000000",
"332331021001303111123330202130103102130331221",
"321001231300102311033030010023030111222311010"]);

y:=CambridgeMatrix(1,F,45,[
"001000000000000000000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"000000010000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"100110011000000000000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"111011010000000000000000000000000000000000000",
"010011001000000000000000000000000000000000000",
"000000000000010000000000000000000000000000000",
"000000000000000100000000000000000000000000000",
"000000000000000010000000000000000000000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000010000000000000000000000000",
"000000000000000000001000000000000000000000000",
"000000000000000000000010000000000000000000000",
"000000000000000000000000100000000000000000000",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000100000000000000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000010000000000000",
"000000000000000000000000000000001000000000000",
"000000100000000000000000000000000000000000000",
"000000000000000000000000000000000010000000000",
"000000000000000000000000000000000000100000000",
"000000000000000000000000000000000000010000000",
"000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000001000",
"033311103000130023030132211231111033213113000",
"000000000100000000000000000000000000000000000",
"000000000000000000000000000000000000000000010",
"000000000000000000000000000000000000000000001",
"000000000101000000010100100000000000000000000",
"330210212312313311310200130211022311213020301",
"132213111100101320013222322113031012201203110",
"110000130120100132101330320203221120331322213",
"000000000001000000000000000000000000000000000",
"230013120322102230221211220220013023202303220",
"323010320301112200132122101222230220231200031",
"000000000000100000000000000000000000000000000",
"201122320013110312112112013230131133233300031",
"130030033212200200131203102322300133220030032",
"121332123330332100311021130003302002223133232",
"332310020002022323213122222030030103211020330",
"000000000000001000000000000000000000000000000"]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is 3.M22 < GL(45,GF(4))";