local z, r, result; result := rec(); result.comment := "L2(89) as 90 x 90 monomial matrices over Z(z44)\n"; # Change the value of r to any number between 1 and 21 # to get the complete set of inequivalent faithful irreducible 90-dimensional # representations of L2(89) r := 1; z := E(44)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(90) ]; result.centralizeralgebra := [ IdentityMat(90) ]; result.generators := [ DiagonalMat([z^27,z^38,z^20,z^24,z^10,z^7,z^42,z^17,z^3,z^28,z^26, z^31,z^8,z^9,z^30,z^23,z^15,z^19,z^38,z^5,z^31,z^40,z^11,z^39,z^29, z^2,z^34,z^14,z^9,z^16,-1,1,z^42,z^20,z^14,z^15,z^33,z^2,z^26,z^34, z^36,z^5,1,z^17,z^8,z^18,z^41,z^12,z^39,z^18,z^43,z^43,z^6,z^35, z,z^4,z^16,z^13,z^40,z^10,z^13,z^24,z^29,z^35,z^25,z^12,z^40,z^11, z^23,z^32,z^25,z^19,z^7,z^3,z^32,z^4,z^6,z^37,z^33,-1,z^36,z^28, z^27,z,z^21,z^37,z^21,z^41,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^10,z^25,1,z^30,z^11,z^9,z^14,z^35,z^36,z^13,z^6,z^42, z^2,z^21,z^32,z^14,z^23,z^38,-1,z^12,z^29,z^17,z^41,z^36,z^43,z^5, z^27,z^25,z^3,z^41,z^42,z^16,z^29,z^9,z^17,z^19,z^32,z^27,1,z^35, z,z^24,z^39,-1,z,z^26,z^26,z^33,z^18,z^28,z^31,z^43,z^40,z^23,z^37, z^40,z^7,z^12,z^18,z^8,z^39,z^18,z^38,z^6,z^15,z^8,z^2,z^34,z^30, z^15,z^31,z^33,z^20,z^16,z^5,z^19,z^11,z^10,z^28,z^4,z^20,z^4,z^24, z^13,z^21,z^3,z^7,z^37,z^34,z^26]) * 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;