/*
2"U4(3).D8 as 6 x 6 matrices over GF(3).
Elements in this group satisfy g*Tranpose(g) = I or -I.
*/

F:=GF(3);

x:=CambridgeMatrix(1,F,6,[
"100000",
"010000",
"001000",
"000100",
"000010",
"000002"]);

y:=CambridgeMatrix(1,F,6,[
"010010",
"001001",
"100100",
"100200",
"010020",
"001002"]);

G<x,y>:=MatrixGroup<6,F|x,y>;
z:=y^6; // Central involution.