local z, r, result; result := rec(); result.comment := "2.L2(193) as 194 x 194 monomial matrices over Z(z192)\n"; # Change the value of r to any number between 1 and 48 # to get the complete set of inequivalent faithful irreducible 194-dimensional # representations of 2.L2(193) r := 1; z := E(192)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(194) ]; result.centralizeralgebra := [ IdentityMat(194) ]; result.generators := [ DiagonalMat([z^147,z^8,z^140,z^60,z^95,z^132,z^170,z^167,z^14,z^181, z,z^115,z^42,z^26,z^172,z^146,z^151,z^13,z^176,z^141,z^184,z^161, z^82,z^183,z^53,z^56,z^49,z^135,z^104,z^169,z^46,z^79,z^11,z^126, z^16,z^149,z^99,z^81,z^108,z^174,1,z^155,z^80,z^3,z^175,z^57,z^93, z^74,z^7,z^171,z^188,z^45,z^103,z^20,-1,z^163,z^129,z^59,z^185,z^23, z^128,z^134,z^130,z^67,z^157,z^43,z^65,z^21,z^55,z^83,z^28,z^22, z^47,z^92,z^107,z^179,z^64,z^51,z^75,z^35,z^37,z^190,z^152,z^116, z^3,z^62,z^162,z^138,z^9,z^38,z^90,z^154,z^78,z^85,z^136,z^186,z^40, z^144,z^117,z^6,z^100,z^19,z^27,z^68,z^191,z^97,z^77,z^121,z^168, z^153,z^148,z^159,z^98,z^84,z^10,z^112,z^143,z^72,z^73,z^24,z^34, z^66,z^87,z^127,z^69,z^124,z^114,z^17,z^105,z^12,z^187,z^133,z^25, z^145,z^165,z^122,z^36,z^166,z^30,z^113,z^29,z^164,z^33,z^118,z^160, z^139,z^18,z^125,z^178,z^2,z^94,z^5,z^101,z^110,z^54,z^111,z^70, z^48,z^15,z^4,z^52,z^50,z^120,z^88,z^177,z^58,z^71,z^131,z^119,z^123, z^137,z^89,z^44,z^63,z^156,z^32,z^182,z^173,z^61,z^158,z^76,z^102, z^189,z^142,z^91,z^39,z^31,z^106,z^41,z^180,z^150,z^86,z^109,z^93 ]) * PermutationMat( ( 1, 20)( 2,164)( 3,111)( 4,137)( 5, 11)( 6,175)( 7,144)( 8,108) ( 9, 23)( 10, 75)( 12,178)( 13,155)( 14,157)( 15, 84)( 16,184)( 17,171) ( 18, 70)( 19,116)( 21, 29)( 22,124)( 24,129)( 25, 66)( 26, 97)( 27, 73) ( 28,110)( 30,169)( 31,162)( 32,128)( 33, 94)( 34, 87)( 35, 43)( 36,146) ( 37,183)( 38,159)( 39,190)( 40,127)( 41, 55)( 42,132)( 44,194)( 45,140) ( 46,186)( 47, 85)( 48, 72)( 49,172)( 50, 99)( 51,101)( 52, 78)( 53, 59) ( 54,181)( 56,148)( 57,112)( 58, 81)( 60,119)( 61,145)( 62, 92)( 63,180) ( 64,141)( 65,168)( 67,187)( 68, 79)( 69,189)( 71,104)( 74,160)( 76,193) ( 77,176)( 80,179)( 82,113)( 83, 95)( 86,121)( 88,191)( 89,123)( 90,166) ( 91,100)( 93,147)( 96,182)(102,107)(103,125)(105,106)(109,163)(114,130) (115,192)(117,134)(118,120)(122,139)(126,142)(131,153)(133,167)(135,170) (136,138)(143,174)(149,154)(150,151)(152,185)(156,165)(161,173)(177,188), 194) , DiagonalMat([z^150,z^44,z^183,z^153,z^89,z^112,z^11,z^143,z^63,z^98, z^135,z^173,z^170,z^17,z^184,z^4,z^118,z^45,z^29,z^175,z^149,z^154, z^16,z^179,z^144,z^187,z^164,z^85,z^186,z^56,z^59,z^52,z^138,z^107, z^172,z^49,z^82,z^14,z^129,z^19,z^152,z^102,z^84,z^111,z^177,z^3, z^158,z^83,z^187,z^178,z^60,-1,z^77,z^10,z^174,z^191,z^48,z^106, z^23,z^99,z^166,z^132,z^62,z^188,z^26,z^131,z^137,z^133,z^70,z^160, z^46,z^68,z^24,z^58,z^86,z^31,z^25,z^50,z^95,z^110,z^182,z^67,z^54, z^78,z^38,z^40,z,z^155,z^119,z^6,z^65,z^165,z^141,z^12,z^41,z^93, z^157,z^81,z^88,z^139,z^189,z^43,z^147,z^120,z^9,z^103,z^22,z^30, z^71,z^2,z^100,z^80,z^124,z^171,z^156,z^151,z^162,z^101,z^87,z^13, z^115,z^146,z^75,z^76,z^27,z^37,z^69,z^90,z^130,z^72,z^127,z^117, z^20,z^108,z^15,z^190,z^136,z^28,z^148,z^168,z^125,z^39,z^169,z^33, z^116,z^32,z^167,z^36,z^121,z^163,z^142,z^21,z^128,z^181,z^5,z^97, z^8,z^104,z^113,z^57,z^114,z^73,z^51,z^18,z^7,z^55,z^53,z^123,z^91, z^180,z^61,z^74,z^134,z^122,z^126,z^140,z^92,z^47,z^66,z^159,z^35, z^185,z^176,z^64,z^161,z^79,z^105,1,z^145,z^94,z^42,z^34,z^109,z^101 ]) * PermutationMat( ( 1, 96, 93)( 2,169,160)( 3,137, 91)( 4, 36, 81)( 5, 57,166)( 6, 27,134) ( 7,102, 33)( 8,142, 54)( 9,151, 24)( 10, 90, 99)( 11,118,139)( 12, 20,148) ( 13,152, 87)( 14, 40,115)( 15, 37, 17)( 16, 82,149)( 18, 86, 34)( 19, 72, 79) ( 21,154, 83)( 22, 70, 69)( 23, 51,145)( 25,106, 67)( 26,161, 48)( 28, 41,103) ( 29,190,158)( 30,105,131)( 31, 89, 38)( 32,181,187)( 35, 92,178)( 39,120, 78) ( 42,104,117)( 43,138,112)( 44,173,100)( 45,164,101)( 46, 55,135)( 47, 71,170) ( 49,194, 52)( 50,162, 68)( 53,110,159)( 56,114,107)( 58,185,132)( 59,127,111) ( 60,191,163)( 61,144,182)( 62,183,124)( 63,129,188)( 64,109,141)( 65,165,180) ( 66, 73,126)( 74, 98,167)( 75,123, 76)( 77,175, 95)( 80,157,172)( 84,155,193) ( 85,174,146)( 88,140,171)( 94,122,192)( 97,176,119)(108,130,128)(113,150,156) (116,179,147)(121,186,136)(125,133,189)(143,177,168), 194)]; return result;