local z, r, result;

result := rec();

result.comment := "L2(83) as 84 x 84 monomial matrices over Z(z41)\n";

# Change the value of r to any number between 1 and 20
# to get the complete set of inequivalent faithful irreducible 84-dimensional
# representations of L2(83)
r := 1;
z := E(41)^r;

result.symmetricforms := [ ]; 
result.antisymmetricforms := [ ]; 
result.hermitianforms := [ IdentityMat(84) ];
result.centralizeralgebra := [ IdentityMat(84) ];

result.generators := [
DiagonalMat([z^14,z^38,z^2,z^18,z^37,z^21,z^39,z^10,1,z^10,z^17,z^30,
  z^7,z^11,z^40,z^20,z^22,z^36,z^7,z^23,z^31,z^16,z^15,z^13,z^28,z^31,
  z^36,z^32,z^22,z,z^9,z^26,z^15,z^36,z^14,z^24,z^6,z^38,z^17,z^26,
  z^29,z^23,z^19,z^3,z^4,z^4,z^18,z^9,z^33,z^20,z^5,z^2,z^21,z^32,
  z^27,z^8,z^35,z^27,z^16,z^25,z^12,z^34,z^8,z^29,z^12,z^6,z^19,z,
  z^39,z^5,z^3,z^37,z^30,z^25,z^13,z^24,z^28,z^34,z^40,1,z^33,z^35,
  z^11,z^5]) *
PermutationMat(
( 1,58)( 2,71)( 3, 7)( 4,42)( 5,46)( 6,50)( 8,21)( 9,80)(10,26)(11,36)(12,83)
(13,62)(14,73)(15,68)(16,53)(17,67)(18,70)(19,78)(20,47)(22,74)(23,40)(24,77)
(25,75)(27,51)(28,31)(29,43)(30,79)(32,33)(34,84)(35,55)(37,57)(38,44)(39,76)
(41,65)(45,72)(48,54)(49,63)(52,69)(56,81)(59,60)(61,64)(66,82), 84)
,
DiagonalMat([z^25,z^40,z^34,z^30,z^14,z^15,z^15,z^29,z^20,z^3,z^31,
  z^16,z^13,z^32,z^2,z^38,z^19,z^5,z^38,z^27,z^36,z^23,z^4,z^19,z^40,
  z^23,z^17,z^30,z^12,z^9,z^16,z^14,z^7,1,z^36,z^24,z^35,z^39,z^4,
  z^10,z^11,z^3,z^5,z^22,z^8,z^13,z^29,z^7,z^32,z^9,z^21,z^11,z^21,
  z^28,1,z^18,z^22,z^10,z^31,z^33,z^6,z^18,z^34,z,z^27,z^26,z^24,z^39,
  z,z^6,z^2,z^33,z^12,z^20,z^37,z^26,z^23,z^25,z^35,z^17,z^8,z^28,
  z^37,z^18]) *
PermutationMat(
( 1,57,79)( 2,69,34)( 3,54,74)( 4, 6,83)( 5,78,15)( 7,17,33)( 8,71,58)
( 9,62,42)(10,72,43)(11,68,29)(12,70,24)(13,39,67)(14,32,21)(16,22,53)
(18,65,50)(19,35,45)(20,38,31)(23,66,41)(25,52,59)(26,61,73)(27,75,82)
(28,64,40)(30,36,81)(37,56,47)(44,76,63)(46,48,51)(49,60,80)(55,77,84), 84)];

return result;