local z, r, result;

result := rec();

result.comment := "2.L2(61) as 62 x 62 monomial matrices over Z(z60)\n";

# Change the value of r to any number between 1 and 15
# to get the complete set of inequivalent faithful irreducible 62-dimensional
# representations of 2.L2(61)
r := 1;
z := E(60)^(2*r-1);

result.symmetricforms := [ ]; 
result.antisymmetricforms := [ ]; 
result.hermitianforms := [ IdentityMat(62) ];
result.centralizeralgebra := [ IdentityMat(62) ];

result.generators := [
DiagonalMat([z^40,z^33,z^25,z^45,z^46,z^16,z^54,z^36,z^41,z^12,z^10,
  z^4,z^21,z^42,z^11,z^9,z^48,z^55,z^13,z^50,z^22,z^7,z^23,z^59,z^47,
  z^15,z^27,z^29,z^37,z^12,z^5,z^8,z^58,z^44,z^24,z^57,z^31,z^20,z^35,
  z^39,z^34,z^18,z^28,z^53,z^19,z^38,z^51,1,z^56,z^2,z^26,z^17,z^14,
  z,z^32,z^43,z^6,z^49,z^3,-1,z^52,z^18]) *
PermutationMat(
( 1,20)( 2,36)( 3,31)( 5,34)( 6,53)( 7, 8)( 9,58)(10,62)(11,38)(12,51)(13,16)
(14,17)(15,45)(18,39)(19,52)(21,32)(22,23)(24,37)(25,56)(27,59)(28,54)(29,44)
(30,42)(33,55)(35,57)(40,47)(41,49)(43,50)(46,61)(48,60), 62)
,
DiagonalMat([z^52,z^4,z^45,z^37,z^57,z^58,z^28,z^6,z^48,z^53,z^59,
  z^22,z^16,z^33,z^54,z^23,z^21,1,z^7,z^25,z^2,z^34,z^19,z^35,z^11,
  z^59,z^27,z^39,z^41,z^49,z^24,z^17,z^20,z^10,z^56,z^36,z^9,z^43,
  z^32,z^47,z^51,z^46,-1,z^40,z^5,z^31,z^50,z^3,z^12,z^8,z^14,z^38,
  z^29,z^26,z^13,z^44,z^55,z^18,z,z^15,z^42,z^31]) *
PermutationMat(
( 1, 6,34)( 2,38,55)( 3, 4,52)( 5,17,61)( 7,54, 8)( 9,23,10)(11,62,43)
(12,16,60)(13,14,25)(15,22,39)(18,53,46)(19,29,49)(20,36,26)(21,50,47)
(24,59,31)(27,56,30)(28,48,58)(32,35,40)(37,42,45)(41,57,51), 62)];

return result;