/*
Realisation of the presentation of S8(2) in S82P1 as 8 x 8 matrices over GF(2).

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

F:=FiniteField(2);

x:=CambridgeMatrix(1,F,8,[
"10000000",
"01000000",
"00100000",
"10010000",
"10001000",
"10000100",
"10000010",
"00000001"]);

y:=CambridgeMatrix(1,F,8,[
"01000000",
"00100000",
"00010000",
"00001000",
"00000100",
"00000010",
"00000001",
"11111111"]);

G<x,y>:=MatrixGroup<8,F|x,y>;

B:=CambridgeMatrix(1,F,8,[
"00011110",
"00001111",
"00000111",
"10000011",
"11000001",
"11100000",
"11110000",
"01111000"]);