local z, r, result; result := rec(); result.comment := "2.L2(179) as 180 x 180 monomial matrices over Z(z178)\n"; # Change the value of r to any number between 1 and 44 # to get the complete set of inequivalent faithful irreducible 180-dimensional # representations of 2.L2(179) r := 1; z := E(178)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(180) ]; result.centralizeralgebra := [ IdentityMat(180) ]; result.generators := [ DiagonalMat([z^79,z^82,z^62,z^31,z^59,z^54,z^22,z^15,-1,z^151,z^80, -1,z^168,z^60,z^175,z^100,z^106,z^137,z^141,z^112,z^142,z^161,z^123, z^63,z^177,z^131,z^29,z^67,z^88,z^120,z^77,z^86,z^143,z^159,z^93, z^12,z^85,z^111,z^136,z^18,z^10,z^97,z^105,z^110,z^127,z^90,z^171, z^32,z^176,z^165,z^2,z^37,z^109,z^39,z^20,z^113,z^160,z^146,z^43, z^87,z^148,z^64,z^156,z^102,z^3,z^129,z^19,z^140,z^84,z^104,z^36, z^24,z^51,z^99,z^96,z^83,1,z^155,z^55,z^174,z^50,z^8,z^9,z^98,z^138, z^162,z^158,z^26,z^40,z^126,z^14,z^66,z^42,z^76,z^11,z^139,z^95, z^44,z^121,z^150,z^78,z^149,z^119,z^41,z^91,z^134,z^5,z^69,z^34, z^57,z^4,z^115,z^28,z^13,z^144,z^147,z^122,z^81,z^169,z^167,z^30, z^153,z^33,z^132,z^154,z^58,z^70,z^72,z^23,z^173,z^6,z^73,z^52,z^107, z^163,z^94,z^145,z^65,z^118,z^25,z^108,z^46,z,z^103,z^116,z^68,z^152, z^170,z^61,z^166,z^130,z^114,z^124,z^157,z^117,z^35,z^71,z^53,z^47, z^38,z^128,z^135,z^74,z^48,z^21,z^125,z^27,z^92,z^75,z^17,z^7,z^49, z^16,z^172,z^133,z^56,z^101,z^164,z^45,1]) * PermutationMat( ( 1, 41)( 2,171)( 3,167)( 4,126)( 5,121)( 6,156)( 7, 28)( 8,163) ( 9, 77)( 10,145)( 11, 83)( 12,180)( 13, 74)( 14, 27)( 15,168)( 16,120) ( 17, 22)( 18,151)( 19, 90)( 20, 78)( 21,166)( 23,115)( 24, 88)( 25, 46) ( 26, 39)( 29,143)( 30,116)( 31, 36)( 32, 65)( 33,153)( 34,141)( 35, 80) ( 37,111)( 38, 63)( 40,157)( 42,148)( 43, 86)( 44,154)( 45, 68)( 47, 75) ( 48,110)( 49,105)( 50, 64)( 51, 60)( 52,133)( 53, 87)( 54, 81)( 55,108) ( 56,125)( 57,134)( 58, 99)( 59,142)( 61,103)( 62,140)( 66, 85)( 67,127) ( 69,107)( 70,135)( 71,158)( 72,138)( 73,160)( 76,131)( 79,109)( 82,118) ( 84,119)( 89,172)( 91,169)( 92,129)( 93,159)( 94,114)( 95,101)( 96,161) ( 97,174)( 98,179)(100,155)(102,139)(104,164)(106,175)(112,147)(113,149) (117,137)(122,152)(123,176)(124,162)(128,170)(130,136)(132,173)(144,178) (146,165)(150,177), 180) , DiagonalMat([z^21,z^53,z^78,z^138,z^130,z^39,z^47,z^52,z^69,z^32,z^113, z^152,z^118,z^107,z^122,z^157,z^51,z^159,z^140,z^55,z^102,z^88,z^163, z^29,z^90,z^6,z^98,z^44,z^123,z^71,z^139,z^82,z^26,z^46,z^156,z^144, z^171,z^41,z^38,z^25,z^120,z^97,z^175,z^116,z^170,z^128,z^129,z^40, z^80,z^104,z^100,z^146,z^160,z^68,z^134,z^8,z^162,z^18,z^131,z^81, z^37,z^164,z^63,z^92,z^20,z^91,z^61,z^161,z^33,z^76,z^125,z^11,z^154, z^177,z^124,z^57,z^148,z^133,z^86,-1,z^64,z^23,z^111,z^109,z^150, z^95,z^153,z^74,z^96,1,z^12,z^14,z^143,z^115,z^126,z^15,z^172,z^49, z^105,z^36,z^87,z^7,z^60,z^145,z^50,z^166,z^121,z^45,z^58,z^10,z^94, z^112,z^3,z^108,z^72,z^56,z^66,z^99,z^59,z^155,z^13,z^173,z^167, z^158,z^70,z^77,z^16,z^168,z^141,z^67,z^147,z^34,z^17,z^137,z^127, z^169,z^136,z^114,z^75,z^176,z^43,z^106,z^165,z^24,z^4,z^151,z,z^174, z^142,z^135,z^31,z^93,z^22,z^5,z^110,z^2,z^117,z^42,z^48,z^79,z^83, z^54,z^84,z^103,z^65,z^5,z^119,z^73,z^149,z^9,z^30,z^62,z^19,z^28, z^85,z^101,z^35,z^132,z^27,z^84]) * PermutationMat( ( 1, 23, 97)( 2,123,137)( 3, 20,108)( 4,124,103)( 5,167, 14)( 6,177, 50) ( 7,156, 47)( 8, 55, 45)( 9,179, 32)( 10,172,163)( 11,153,141)( 12,142, 27) ( 13, 65, 48)( 15,134, 42)( 16, 26, 96)( 17, 75,113)( 18, 58,147)( 19,106,105) ( 21,170,130)( 22, 25, 90)( 24,166, 36)( 28, 95, 56)( 29, 51, 78)( 30,119,159) ( 31, 88, 93)( 33, 49,115)( 34, 57, 77)( 35,165,150)( 37, 79,118)( 38,116, 60) ( 39, 46, 91)( 40, 54,175)( 41, 94,107)( 43,162,135)( 44, 52,111)( 53,173, 74) ( 59, 98,140)( 61,139,117)( 62,128,144)( 63,109, 76)( 64,102,160)( 66,125,133) ( 67,104, 85)( 68,114,101)( 69,157,174)( 70, 83,136)( 71,158, 72)( 73,110, 92) ( 80,154,180)( 81,151,161)( 82,149,121)( 84, 89,146)( 86,131,138)( 87,152,155) ( 99,126,148)(100,120,143)(112,164,129)(122,169,132)(127,178,171)(145,176,168), 180)]; return result;