/*
www-ATLAS of Group Representations.
L3(4):2a 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",
"000000000000000000000000000010000000000000000",
"000000000000001000000000000000000000000000000",
"010600100000000000100060000000000000000000000",
"106010000000100000000600000000000000000000000",
"000000000000000010000000000000000000000000000",
"000000000000000000000000000000000100000000000",
"000000000000000001000000000000000000000000000",
"000000000000000000000000000000000001000000000",
"000000000000000000000000000000000000010000000",
"000000000000000000010000000000000000000000000",
"000000000000000000000000000000000000000010000",
"000000000000000000000000000000000000000000100",
"000000000000000000000000000000000000000000001",
"512000531113055424541343614030522556133113143",
"000000000000000000000000100000000000000000000",
"116631665132062461225551664154010113060030006",
"000000000000000000000000001000000000000000000",
"011214315454566124614044621361264364525435120",
"000000000000000000000000000100000000000000000",
"400541554244431663544024101433412035220266112",
"652501040162522006261416505116054460445555321",
"000000000000000000000000000001000000000000000",
"611660100000600000100000600000000100000001000",
"000000000000000000000000000000100000000000000",
"015223504330036254040120315133641155123153051",
"000000000000000000000000000000010000000000000"]);

y:=CambridgeMatrix(1,F,45,[
"001000000000000000000000000000000000000000000",
"066000000000000000000000000000000000000000000",
"000010000000000000000000000000000000000000000",
"000001000000000000000000000000000000000000000",
"106010000000000000000000000000000000000000000",
"000000001000000000000000000000000000000000000",
"000000000100000000000000000000000000000000000",
"000000000010000000000000000000000000000000000",
"000000000000100000000000000000000000000000000",
"000000000000001000000000000000000000000000000",
"000000000000000010000000000000000000000000000",
"000000000000000001000000000000000000000000000",
"000100000000000000000000000000000000000000000",
"000000000000000000010000000000000000000000000",
"000000000000000000000100000000000000000000000",
"000000000000000000000010000000000000000000000",
"000000000000000000000000100000000000000000000",
"000000000000000000000000001000000000000000000",
"000000000000000000000000000100000000000000000",
"000000000000000000000000000001000000000000000",
"000000000000000000000000000000100000000000000",
"000000100000000000000000000000000000000000000",
"000000000000000000000000000000010000000000000",
"000000000000000000000000000000001000000000000",
"000000010000000000000000000000000000000000000",
"000000000000000000000000000000000010000000000",
"000000000000000000000000000000000000100000000",
"000000000000000000000000000000000000001000000",
"000000000000000000000000000000000000000100000",
"000000000000000000000000000000000000000001000",
"000000000000000000000000000000000000000000010",
"244346426255065060310113066214643500622636260",
"165350600452125115132643236316553023511616333",
"062464336161563321040336331025100054004633434",
"221441151003425246366403623343201122601033614",
"230234225433346510651100260223213044300366302",
"000000000001000000000000000000000000000000000",
"204164133313440546565141312624222161423141623",
"664643503642506233611103654232013115236132640",
"141363024336300364323442506025035104356516634",
"564226426241201064354611061610536404502002644",
"000000000000010000000000000000000000000000000",
"364661400162225041300432334563025326616536550",
"200031552306310064036521401153061665440502611",
"650332342115131005611003250003105162404626224"]);

G<x,y>:=MatrixGroup<45,F|x,y>;
print "Group G is L3(4):2a < GL(45,GF(7))";