local z, r, result;

result := rec();

result.comment := "2.L2(89) as 90 x 90 monomial matrices over Z(z88)\n";

# Change the value of r to any number between 1 and 22
# to get the complete set of inequivalent faithful irreducible 90-dimensional
# representations of 2.L2(89)
r := 1;
z := E(88)^(2*r-1);

result.symmetricforms := [ ]; 
result.antisymmetricforms := [ ]; 
result.hermitianforms := [ IdentityMat(90) ];
result.centralizeralgebra := [ IdentityMat(90) ];

result.generators := [
DiagonalMat([z^71,z^82,z^64,z^24,z^54,z^7,z^86,z^17,z^3,z^28,z^26,
  z^31,z^52,z^9,z^74,z^23,z^59,z^63,z^38,z^49,z^75,z^40,z^55,z^39,
  z^73,z^46,z^34,z^58,z^53,z^16,z^66,1,z^42,z^20,z^14,z^15,z^77,z^2,
  z^70,z^78,z^36,z^5,-1,z^61,z^8,z^62,z^41,z^12,z^83,z^18,z^87,z^43,
  z^50,z^79,z,z^48,z^60,z^57,z^84,z^10,z^13,z^68,z^29,z^35,z^25,z^56,
  z^40,z^11,z^67,z^76,z^69,z^19,z^51,z^47,z^32,z^4,z^6,z^81,z^33,z^22,
  z^80,z^72,z^27,z^45,z^21,z^37,z^65,z^85,z^30,z^4]) *
PermutationMat(
( 1,44)( 2,53)( 3,62)( 4,34)( 5,40)( 6,86)( 7,26)( 8,83)( 9,47)(10,30)(11,50)
(12,61)(13,81)(14,64)(15,28)(16,85)(17,25)(18,71)(19,77)(20,49)(21,58)(22,76)
(23,37)(24,42)(27,60)(29,54)(32,43)(33,38)(35,89)(36,63)(39,46)(41,45)(48,75)
(51,84)(52,55)(56,59)(57,82)(65,72)(66,70)(67,90)(68,79)(69,87)(73,78)(74,88), 90)
,
DiagonalMat([z^54,z^69,1,z^74,z^11,z^9,z^14,z^35,z^80,z^57,z^6,z^42,
  z^46,z^21,z^32,z^58,z^23,z^38,z^22,z^56,z^29,z^17,z^41,z^36,z^87,
  z^49,z^71,z^25,z^3,z^85,z^86,z^60,z^73,z^53,z^61,z^19,z^76,z^27,
  -1,z^79,z^45,z^24,z^83,z^66,z,z^70,z^26,z^33,z^62,z^72,z^31,z^43,
  z^40,z^67,z^81,z^84,z^51,z^12,z^18,z^8,z^39,z^62,z^82,z^50,z^59,
  z^52,z^2,z^34,z^30,z^15,z^75,z^77,z^64,z^16,z^5,z^63,z^55,z^10,z^28,
  z^4,z^20,z^48,z^68,z^13,z^65,z^47,z^7,z^37,z^78,z^70]) *
PermutationMat(
( 1,54,77)( 2,30,19)( 3,79,32)( 4,73,18)( 5,55,56)( 6,35,59)( 7,64,42)
( 8,69,17)( 9,86,26)(10,43,24)(11,47,20)(12,31,82)(13,53,67)(14,68,48)
(15,49,63)(16,34,85)(21,74,52)(22,57,81)(23,60,61)(25,84,37)(27,83,88)
(28,33,89)(29,36,44)(38,40,46)(39,62,90)(41,50,65)(45,58,71)(51,66,75)
(70,76,78)(72,80,87), 90)];

return result;