local z, r, result; result := rec(); result.comment := "2.L2(173) as 174 x 174 monomial matrices over Z(z172)\n"; # Change the value of r to any number between 1 and 43 # to get the complete set of inequivalent faithful irreducible 174-dimensional # representations of 2.L2(173) r := 1; z := E(172)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(174) ]; result.centralizeralgebra := [ IdentityMat(174) ]; result.generators := [ DiagonalMat([z^33,z^157,z^104,z^138,z^58,z^21,z^137,z^37,z^27,z^98, z^162,z^23,z^147,z^144,z^123,z^68,z^163,z^54,z^115,z^69,z^49,z^171, z^100,z^89,z^101,z^42,z^160,z^136,z^154,z^168,z^7,z^32,z^6,z^166, z^151,z^132,z^155,z^36,z^94,z^81,z^91,z^161,z^38,z^57,z^102,z^40, z^148,z^52,z^106,z^126,z^128,z^3,z^141,z^76,z^4,z^13,z^112,z^167, z^31,z^110,z^75,z^127,z^15,z^84,z^164,z^48,z^87,z^78,z^153,z^111, z^5,z^10,z^83,z^67,z^97,z^90,z^41,z^19,z^70,z^45,z^72,z^131,z^135, z^77,z^11,z^165,1,z^43,z^39,z^22,z^59,z^60,z^146,z^107,z^16,z^2, z^133,z^29,z^103,z^20,z^159,z^130,z^85,z,z^150,z^71,z^158,z^63,z^125, z^74,z^105,z^62,z^108,z^143,z^113,z^8,z^34,z^23,z^119,z^92,z^24, z^53,z^17,z^142,z^12,z^152,z^30,z^139,z^61,z^145,z^51,z^73,z^156, z^28,z^56,z^88,z^170,z^95,z^26,z^66,z^79,z^169,z^35,z^120,z^118, z^80,z^96,z^99,z^55,z^47,z^64,z^129,z^14,z^9,z^121,z^93,z^117,z^65, -1,z^134,z^140,z^109,z^124,z^50,z^44,z^149,z^18,z^114,z^122,z^82, z^25,z^116,z^46,z^63]) * PermutationMat( ( 1,122)( 2, 25)( 3, 29)( 4,144)( 5,134)( 6,158)( 7,155)( 8, 21) ( 9, 91)( 10, 27)( 11,147)( 12,108)( 13, 70)( 14,168)( 15, 83)( 16,167) ( 17,138)( 18, 32)( 19,114)( 20,123)( 22, 67)( 23,107)( 24,142)( 26,165) ( 28,169)( 30, 76)( 31,141)( 33,146)( 34,120)( 35, 94)( 36, 50)( 37, 99) ( 38,164)( 39, 65)( 40, 71)( 41, 58)( 42, 75)( 43, 66)( 44, 98)( 45,133) ( 46,173)( 47, 60)( 48,117)( 49,126)( 51,102)( 52, 73)( 53,157)( 54, 72) ( 55,170)( 56,132)( 57, 93)( 59,149)( 61, 85)( 62, 82)( 63,106)( 64, 96) ( 68,116)( 69,111)( 74, 78)( 77, 80)( 79, 95)( 81,153)( 84,154)( 86,156) ( 87,159)( 89,150)( 90,151)( 92,139)( 97,109)(100,140)(101,148)(103,104) (105,113)(110,125)(112,121)(115,130)(118,174)(119,128)(124,172)(127,135) (129,171)(131,143)(136,137)(145,161)(160,163)(162,166), 174) , DiagonalMat([z^16,z^162,z^15,z^161,z^149,z^134,z^115,z^138,z^19,z^77, z^64,z^74,z^144,z^21,z^40,z^85,z^23,z^131,z^35,z^89,z^109,z^111, z^158,z^124,z^59,z^159,z^168,z^95,z^150,z^14,z^93,z^58,z^110,z^170, z^67,z^147,z^31,z^70,z^61,z^136,z^94,z^160,z^165,z^66,z^50,z^80, z^73,z^24,z^2,z^53,z^28,z^55,z^114,z^118,z^60,z^166,z^148,z^155, z^26,z^22,z^5,z^42,z^43,z^129,z^90,z^171,z^157,z^116,z^12,-1,z^3, z^142,z^113,z^68,z^156,z^133,z^54,z^141,z^46,z^108,z^57,z^88,z^45, z^91,z^126,z^96,z^163,z^17,z^69,z^102,z^75,z^7,z^36,1,z^125,z^167, z^135,z^13,z^122,z^44,z^128,z^34,z^56,z^139,z^11,z^39,z^71,z^153, z^78,z^9,z^49,z^62,z^152,z^18,z^103,z^101,z^63,z^79,z^82,z^38,z^30, z^47,z^112,z^169,z^164,z^104,z^76,z^100,z^48,z^69,z^117,z^123,z^92, z^107,z^33,z^27,z^132,z,z^97,z^105,z^65,z^8,z^99,z^29,z^140,z^87, z^121,z^41,z^4,z^120,z^20,z^10,z^81,z^145,z^6,z^130,z^127,z^106, z^51,z^146,z^37,z^98,z^52,z^32,z^154,z^83,z^72,z^84,z^25,z^143,z^119, z^137,z^151,z^17]) * PermutationMat( ( 1,140,159)( 2,163,156)( 3,144,101)( 4, 90,153)( 5, 46, 7)( 6,121,142) ( 8, 97,107)( 9,110, 13)( 10,155, 20)( 11, 52, 50)( 12, 24,160)( 14, 60, 64) ( 15,117,130)( 16,146, 94)( 17, 81,133)( 18, 61, 93)( 19,145,124)( 21,137,115) ( 22, 82,154)( 23,134,118)( 25,123,138)( 26, 27, 88)( 28,166, 56)( 29,173, 63) ( 30, 31,141)( 32, 91,106)( 33, 45, 69)( 34,111, 95)( 35, 75,147)( 36,114, 92) ( 37, 74, 47)( 38,105, 84)( 39,136,168)( 40, 96,148)( 41,135, 83)( 42, 99,112) ( 43,165,169)( 44,119, 48)( 49,122,132)( 51, 87,108)( 53, 76,139)( 54,128, 85) ( 55, 73, 66)( 57, 65,158)( 58,149, 98)( 59,129,162)( 62,150,152)( 67,100,170) ( 68,113,127)( 70, 89,174)( 71,164,172)( 72,120,125)( 77, 79,167)( 78,143,126) ( 80,171,131)( 86,151,103)(102,116,161)(104,109,157), 174)]; return result;