/*
Realisation of the presentation of U5(2) in U52P1 as 5 x 5 matrices over GF(4).

The generators are x and y and the Hermitian form is given by B.
*/

F<w>:=FiniteField(4);
W:=w^2;

x:=CambridgeMatrix(1,F,5,[
"10000",
"31000",
"10100",
"10010",
"20001"]);

y:=CambridgeMatrix(1,F,5,[
"01000",
"00100",
"00010",
"00001",
"10000"]);

G<x,y>:=MatrixGroup<5,F|x,y>;

B:=CambridgeMatrix(1,F,5,[
"02113",
"30211",
"13021",
"11302",
"21130"]);