/*
www-ATLAS of Group Representations.
J1 represented as 31 x 31 matrices over GF(7).
*/

F:=GF(7);

x:=CambridgeMatrix(1,F,31,[
"2400000000000000000000000000000",
"1500000000000000000000000000000",
"2512000000000000000000000000000",
"5206000000000000000000000000000",
"0114120000000000000000000000000",
"6166060000000000000000000000000",
"5623213150000000000000000000000",
"3644324313000000000000000000000",
"5130246315000000000000000000000",
"4506214260000000000000000000000",
"4566365406253000000000000000000",
"0011661334020100000000000000000",
"5113630664655300000000000000000",
"3423615213040500000000000000000",
"4266250523454204200000000000000",
"1245220640526462034000000000000",
"5316316110220363016000000000000",
"0400461013501142255552000000000",
"0365120332660014603552000000000",
"5502651225250060050520040000000",
"0641030251516363554446101000000",
"2334622645224353212523141000000",
"3462024113061411110613601466000",
"2356064201104024664555323000000",
"6152062400516033555230523311000",
"3322045233451312226200151214263",
"6054264153432615355420262104210",
"2044122461606410350560431660625",
"3132235222351412644551102210361",
"0552436315462341036520205523323",
"6505350006115252102141153534361"]);

y:=CambridgeMatrix(1,F,31,[
"2200000000000000000000000000000",
"5450000000000000000000000000000",
"6510000000000000000000000000000",
"4635500000000000000000000000000",
"3203036000000000000000000000000",
"2006322100000000000000000000000",
"3230001300000000000000000000000",
"1442005646500000000000000000000",
"3531662546050000000000000000000",
"0112240212310000000000000000000",
"3116233344260000000000000000000",
"5343252640560000000000000000000",
"3340524313112560000000000000000",
"0456406256164061000000000000000",
"5442536534054363140000000000000",
"1445215016654456144500000000000",
"3066333124116346224510000000000",
"1004312061216654261350000000000",
"6331243123564653020316500000000",
"0116303304445224606325300000000",
"6316502360430255031016040500000",
"0313665404542444031531031520000",
"5261543435213224051336000550600",
"2325040240046622012255624606550",
"3051020633603101522524305546165",
"1321133020414002644646444065330",
"3110232010231550002063264421031",
"0061622340536404036313020136031",
"2442023144316643546132462333025",
"6003356350335663436352410331433",
"0565344154011666034045030044015"]);

G<x,y>:=MatrixGroup<31,F|x,y>;
print "Group G is J1 < GL(31,GF(7))";