matrix representation of a permutation in GAP I have wrote the following lines in GAP:

$ gap> G:=PSL(4,4);\\
<permutation~group~of~size~987033600~with~2~generators>\\
gap> p:=SylowSubgroup(G,5);;\\
gap> e:=Elements(p);;\\
gap> e[2];\\
(2,23,27,31,35)(3,25,26,30,37)(4,24,29,33,36)(5,22,28,32,34)(6,51,43,10,79)(7,50,42,11,80)(8,53,45,12,78)(9,52,44,13,81)(14,18,59,75,55)(15,
19,61,76,57)(16,20,60,74,56)(17,21,58,77,54)(38,65,69,46,84)(39,63,67,47,83)(40,62,66,48,85)(41,64,68,49,82)$

But I need the matrix representation of $e[2]$ as a $4\times 4$ matrix of determinant $1$ over a finite field of order $4$.
How can I find it in GAP?

If you form PSL, you get the permutation action on the projective line.
To get the matrix representation work with SL instead:
gap> G:=SL(4,4);
SL(4,4)
gap> p:=SylowSubgroup(G,5);
<group of 4x4 matrices of size 25 over GF(2^2)>
gap> e:=Elements(p);;
gap> e[2];
[ [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0, 0*Z(2), Z(2)^0 ], 
  [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2^2) ] ]

Please note that the element ordering (i.e. number 2) might not be the same as in the permutation representation.
