local z, r, result; result := rec(); result.comment := "2.L2(83) as 84 x 84 monomial matrices over Z(z82)\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 2.L2(83) r := 1; z := E(82)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(84) ]; result.centralizeralgebra := [ IdentityMat(84) ]; result.generators := [ DiagonalMat([z^55,z^38,z^43,z^18,z^37,z^21,z^80,z^10,1,z^51,z^17,z^71, z^7,z^11,z^40,z^61,z^63,z^77,z^48,z^64,z^31,z^57,z^15,z^13,z^69, z^72,z^36,z^73,z^22,z^42,z^50,z^67,z^56,z^77,z^14,z^24,z^6,z^79, z^58,z^26,z^70,z^23,z^19,z^44,z^45,z^4,z^59,z^9,z^74,z^20,z^5,z^2, z^62,z^32,z^27,z^8,z^35,z^68,z^16,z^25,z^12,z^34,z^49,z^29,z^53, z^47,z^60,z,z^39,z^46,z^3,z^78,z^30,z^66,z^54,z^65,z^28,z^75,z^81, -1,z^33,z^76,z^52,z^46]) * 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^75,z^71,z^14,z^15,z^56,z^29,z^61,z^44,z^72, z^57,z^54,z^32,z^2,z^79,z^60,z^5,z^38,z^68,z^77,z^64,z^4,z^19,z^81, z^23,z^17,z^30,z^53,z^9,z^16,z^55,z^48,1,z^36,z^24,z^35,z^80,z^45, z^51,z^11,z^3,z^46,z^22,z^8,z^13,z^70,z^7,z^73,z^50,z^62,z^52,z^21, z^69,-1,z^59,z^63,z^10,z^31,z^33,z^47,z^18,z^34,z,z^27,z^67,z^65, z^39,z^42,z^6,z^43,z^74,z^12,z^20,z^37,z^26,z^64,z^66,z^76,z^58, z^49,z^28,z^78,z^59]) * 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;