gap> g:=[[0,5,5,4],[0,0,5,5],[6,4,4,4],[3,3,1,3]]*One(GF(7));
[ [ 0*Z(7), Z(7)^5, Z(7)^5, Z(7)^4 ], [ 0*Z(7), 0*Z(7), Z(7)^5, Z(7)^5 ], 
  [ Z(7)^3, Z(7)^4, Z(7)^4, Z(7)^4 ], [ Z(7), Z(7), Z(7)^0, Z(7) ] ]
gap> Display(g);
 . 5 5 4
 . . 5 5
 6 4 4 4
 3 3 1 3
gap> Order(g);
200
gap> h:=g^77;
[ [ Z(7)^2, Z(7)^2, Z(7), Z(7)^3 ], [ Z(7)^0, Z(7)^2, Z(7)^2, Z(7) ], 
  [ Z(7), Z(7)^4, Z(7), Z(7)^4 ], [ Z(7)^4, Z(7)^3, Z(7)^5, Z(7)^5 ] ]

gap> g5:=g^8;Order(g5);
[ [ Z(7)^5, 0*Z(7), Z(7), 0*Z(7) ], [ Z(7)^3, Z(7)^5, 0*Z(7), Z(7) ], 
  [ Z(7)^3, Z(7)^3, Z(7)^3, 0*Z(7) ], [ 0*Z(7), Z(7)^3, 0*Z(7), Z(7)^3 ] ]
25
gap> h5:=h^8;Order(h5);
[ [ Z(7)^0, Z(7)^4, Z(7)^5, 0*Z(7) ], [ Z(7)^4, Z(7)^0, Z(7)^4, Z(7)^5 ], 
  [ Z(7)^4, Z(7), Z(7)^5, Z(7)^4 ], [ Z(7)^0, Z(7), 0*Z(7), Z(7)^5 ] ]
25

gap> a:=g5^5;b:=h5^5;
[ [ Z(7)^4, Z(7)^0, Z(7)^2, Z(7)^0 ], [ Z(7)^0, Z(7)^4, Z(7)^0, Z(7)^2 ], 
  [ Z(7)^3, Z(7)^3, 0*Z(7), Z(7)^3 ], [ Z(7)^2, Z(7)^4, Z(7)^2, Z(7)^5 ] ]
[ [ Z(7), Z(7), Z(7)^4, Z(7)^2 ], [ Z(7)^4, Z(7), Z(7), Z(7)^4 ], 
  [ 0*Z(7), Z(7)^5, Z(7)^2, Z(7)^3 ], [ Z(7)^3, Z(7)^0, Z(7)^4, Z(7)^5 ] ]

gap> First([0..4],x->a^x=b);
2

gap> giant:=List([0..2],x->a^(x*2));
[ [ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ], 
      [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ] ]
    , [ [ Z(7), Z(7), Z(7)^4, Z(7)^2 ], [ Z(7)^4, Z(7), Z(7), Z(7)^4 ], 
      [ 0*Z(7), Z(7)^5, Z(7)^2, Z(7)^3 ], [ Z(7)^3, Z(7)^0, Z(7)^4, Z(7)^5 ] ]
    , [ [ Z(7)^5, Z(7)^5, Z(7)^2, Z(7) ], [ Z(7)^3, Z(7)^5, Z(7)^5, Z(7)^2 ], 
      [ 0*Z(7), Z(7), Z(7)^0, Z(7)^3 ], [ Z(7), Z(7)^4, Z(7)^3, Z(7)^2 ] ] ]

gap> baby:=List([0..2],x->b*a^-x);
[ [ [ Z(7), Z(7), Z(7)^4, Z(7)^2 ], [ Z(7)^4, Z(7), Z(7), Z(7)^4 ], 
      [ 0*Z(7), Z(7)^5, Z(7)^2, Z(7)^3 ], [ Z(7)^3, Z(7)^0, Z(7)^4, Z(7)^5 ] ] , 
  [ [ Z(7)^4, Z(7)^0, Z(7)^2, Z(7)^0 ], [ Z(7)^0, Z(7)^4, Z(7)^0, Z(7)^2 ], 
      [ Z(7)^3, Z(7)^3, 0*Z(7), Z(7)^3 ], [ Z(7)^2, Z(7)^4, Z(7)^2, Z(7)^5 ] ] , 
  [ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ], 
      [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ] ] ]
gap> is:=Intersection(giant,baby)[1];
[ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ], 
  [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ] ]
gap> Position(giant,is);
1
gap> Position(baby,is);
3
gap> e0:=2;
2

gap> h5:=h5/g5^2;
[ [ Z(7)^0, 0*Z(7), 0*Z(7), 0*Z(7) ], [ 0*Z(7), Z(7)^0, 0*Z(7), 0*Z(7) ], 
  [ 0*Z(7), 0*Z(7), Z(7)^0, 0*Z(7) ], [ 0*Z(7), 0*Z(7), 0*Z(7), Z(7)^0 ] ]
gap> Order(h5);
1

gap> e5:=2;
2


gap> g2:=g^25;Order(g2);
[ [ Z(7), Z(7)^0, Z(7), Z(7) ], [ 0*Z(7), Z(7), Z(7)^0, Z(7) ], 
  [ Z(7)^0, Z(7)^5, Z(7)^4, Z(7)^2 ], [ Z(7)^2, Z(7)^3, Z(7)^3, Z(7)^5 ] ]
8
gap> h2:=h^25;Order(h2);
[ [ Z(7)^4, Z(7)^3, Z(7)^4, Z(7)^4 ], [ 0*Z(7), Z(7)^4, Z(7)^3, Z(7)^4 ], 
  [ Z(7)^3, Z(7)^2, Z(7), Z(7)^5 ], [ Z(7)^5, Z(7)^0, Z(7)^0, Z(7)^2 ] ]
8
gap> e2:=First([1,3,5,7],x->g2^x=h2);
5
gap> ChineseRem([25,8],[e5,e2]);
77