local z, r, result; result := rec(); result.comment := "2.L2(191) as 192 x 192 monomial matrices over Z(z190)\n"; # Change the value of r to any number between 1 and 47 # to get the complete set of inequivalent faithful irreducible 192-dimensional # representations of 2.L2(191) r := 1; z := E(190)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(192) ]; result.centralizeralgebra := [ IdentityMat(192) ]; result.generators := [ DiagonalMat([z^36,z^73,z^99,z^8,z^53,z^24,z^27,z^84,z^91,z^52,z^114, z^181,z^67,z^117,z^186,z^75,z^51,z^87,z^18,z^152,z^26,z^60,z^137, z^63,z^143,z^13,z^25,z^96,z^125,z^16,z^34,z^100,z^142,z^150,z^44, z^2,z^119,z^158,z^132,z^130,z^110,z^188,z^156,z^120,z^147,z^169, z^66,z^80,z^77,z^136,z^79,z^58,z^112,z^29,z^126,z^10,z^151,z^31, 1,z^165,z^115,z^81,z^144,z^57,z^104,z^3,z^139,z^106,z^30,z^76,z^64, z^23,z^161,z^32,z^123,z^118,z^111,z^155,z^164,z^39,z^17,z^22,z^35, z^93,z^176,z^160,z^170,z^153,z^48,z^4,z^141,z^64,z^45,z^97,z^140, z^54,z^70,z^59,z^74,z^180,z^121,z^107,z^101,z^122,z^56,z^46,z,z^7, z^11,z^109,z^47,z^98,z^138,z^149,z^102,z^177,z^19,z^72,z^172,z^124, z^20,z^146,z^179,z^38,z^62,z^92,z^21,z^69,z^184,z^86,z^168,z^113, z^133,z^189,z^129,z^131,z^116,z^28,z^5,z^167,z^12,z^43,z^154,z^173, z^174,z^9,z^159,z^41,z^82,z^187,z^178,z^135,z^68,z^49,z^157,z^127, z^55,z^42,z^171,z^90,z^163,z^85,z^50,z^175,z^40,z^108,z^71,z^94, z^14,z^134,z^83,z^6,z^128,z^65,z^103,-1,z^37,z^33,z^61,z^15,z^105, z^78,z^166,z^148,z^185,z^89,z^182,z^88,z^183,z^145,z^162,z^31]) * PermutationMat( ( 1, 98)( 2, 82)( 3, 15)( 4, 18)( 5,158)( 6,167)( 7,153)( 8,109) ( 9, 90)( 10,142)( 11,159)( 12, 65)( 13,138)( 14,131)( 16,121)( 17, 35) ( 19, 49)( 20,133)( 21,128)( 22, 83)( 23,184)( 24, 74)( 25, 33)( 26,149) ( 27, 97)( 28,134)( 29, 86)( 30, 51)( 31,179)( 32,185)( 34,152)( 36, 84) ( 37,183)( 38,156)( 39, 88)( 40, 78)( 41,164)( 42, 94)( 43,135)( 44, 60) ( 45,113)( 46,137)( 47, 54)( 48,180)( 50,114)( 52,177)( 53,144)( 55,147) ( 56,162)( 57,170)( 58, 71)( 59,176)( 61, 87)( 62,169)( 63, 91)( 64,124) ( 66,126)( 67,122)( 68,123)( 69,174)( 70,117)( 72,118)( 73,120)( 75,191) ( 76,140)( 77,145)( 79,101)( 80,105)( 81,182)( 85,110)( 89,111)( 92,192) ( 93,163)( 95,190)( 96,148)( 99,127)(100,181)(102,151)(103,129)(104,161) (106,154)(107,168)(108,188)(112,150)(115,189)(116,166)(119,132)(125,178) (130,146)(136,143)(139,160)(141,171)(155,173)(157,165)(172,186)(175,187), 192) , DiagonalMat([z^131,z^168,z^4,z^103,z^148,z^119,z^122,z^179,z^186,z^147, z^19,z^86,z^162,z^22,z^91,z^170,z^146,z^182,z^113,z^57,z^121,z^155, z^42,z^158,z^48,z^108,z^120,z,z^30,z^111,z^129,z^5,z^47,z^55,z^139, z^97,z^24,z^63,z^37,z^35,z^15,z^93,z^61,z^25,z^52,z^74,z^161,z^175, z^172,z^41,z^174,z^153,z^17,z^124,z^31,z^105,z^56,z^126,-1,z^70, z^20,z^176,z^49,z^152,z^9,z^98,z^44,z^11,z^125,z^171,z^159,z^118, z^66,z^127,z^28,z^23,z^16,z^60,z^69,z^134,z^112,z^117,z^130,z^188, z^81,z^65,z^75,z^58,z^143,z^99,z^46,z^159,z^140,z^2,z^45,z^149,z^165, z^154,z^169,z^85,z^26,z^12,z^6,z^27,z^151,z^141,z^96,z^102,z^106, z^14,z^142,z^3,z^43,z^54,z^7,z^82,z^114,z^167,z^77,z^29,z^115,z^51, z^84,z^133,z^157,z^187,z^116,z^164,z^89,z^181,z^73,z^18,z^38,z^94, z^34,z^36,z^21,z^123,z^100,z^72,z^107,z^138,z^59,z^78,z^79,z^104, z^64,z^136,z^177,z^92,z^83,z^40,z^163,z^144,z^62,z^32,z^150,z^137, z^76,z^185,z^68,z^180,z^145,z^80,z^135,z^13,z^166,z^189,z^109,z^39, z^178,z^101,z^33,z^160,z^8,1,z^132,z^128,z^156,z^110,z^10,z^173, z^71,z^53,z^90,z^184,z^87,z^183,z^88,z^50,z^67,z^126]) * PermutationMat( ( 1,178, 21)( 2, 90, 19)( 3, 55, 22)( 4, 63,133)( 5,113,168)( 6, 91, 44) ( 7, 50,104)( 8, 98, 33)( 9, 40, 71)( 10, 23, 28)( 11, 80, 39)( 12,134,181) ( 13,152,171)( 14,119, 15)( 16, 83,164)( 17, 76,137)( 18, 27,144)( 20,189, 95) ( 24,101,103)( 25, 77, 58)( 26,121,125)( 29,123,159)( 30, 73,166)( 31,105,139) ( 32,177,184)( 34, 82,132)( 35,176,122)( 36,179, 74)( 37,100, 85)( 38,135, 42) ( 41,190, 69)( 43,185,170)( 45,148, 94)( 46,138,188)( 47,172, 72)( 48, 86, 93) ( 49,131,165)( 51,111,147)( 52, 57, 70)( 53, 62,126)( 54,145,149)( 56,167,169) ( 59, 92,192)( 60,175, 81)( 61,180, 78)( 64,106,187)( 65,151, 66)( 67, 99,118) ( 68, 89,136)( 75,102,157)( 79,155,143)( 84,114,142)( 87,116,173)( 88,160,158) ( 96,161,153)( 97,154,183)(107,146,162)(108,124,163)(109,174,117)(110,182,112) (115,191,127)(120,140,129)(128,156,186)(130,150,141), 192)]; return result;