##McLaughlin graph on 275 vertices mclaughlin:=EdgeOrbitsGraph( Group( [ ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9, 12)( 10, 13)( 11, 15)( 14, 19) ( 16, 21)( 17, 22)( 18, 24)( 20, 27)( 23, 31)( 25, 33)( 26, 34)( 28, 37) ( 29, 38)( 30, 40)( 32, 43)( 35, 47)( 36, 48)( 39, 51)( 41, 53)( 42, 54) ( 44, 57)( 45, 58)( 46, 60)( 49, 63)( 50, 64)( 52, 67)( 55, 71)( 56, 72) ( 59, 76)( 61, 78)( 62, 79)( 66, 82)( 68, 85)( 69, 86)( 70, 88)( 73, 92) ( 75, 94)( 77, 97)( 80,101)( 81,102)( 83,105)( 84,106)( 87,110)( 89,112) ( 90,113)( 91,115)( 93,118)( 95,120)( 96,121)( 98,123)( 99,109)(100,125) (103,129)(104,130)(107,133)(108,134)(111,137)(114,140)(116,142)(117,128) (119,144)(122,147)(124,149)(126,139)(131,153)(132,154)(135,158)(136,159) (138,161)(141,164)(143,167)(145,170)(146,172)(148,175)(150,177)(151,178) (152,179)(157,183)(160,187)(162,189)(163,190)(165,168)(166,193)(169,195) (171,196)(174,197)(176,192)(180,204)(181,201)(182,206)(188,209)(191,213) (194,216)(198,221)(199,222)(200,208)(202,225)(203,227)(205,230)(207,232) (210,218)(211,233)(212,235)(215,236)(217,238)(219,240)(220,241)(223,244) (224,245)(226,247)(228,249)(229,250)(231,252)(234,255)(237,257)(239,242) (243,259)(246,261)(248,264)(253,267)(254,268)(256,269)(258,266)(260,270) (262,271)(263,265)(272,274)(273,275), ( 1, 3, 5)( 4, 6, 9)( 7, 10, 14)( 8, 11, 16)( 12, 17, 23) ( 13, 18, 25)( 15, 20, 28)( 19, 26, 35)( 21, 29, 39)( 22, 30, 41) ( 24, 32, 44)( 27, 36, 49)( 31, 42, 55)( 33, 45, 59)( 34, 46, 61) ( 38, 50, 65)( 40, 52, 68)( 43, 56, 73)( 48, 62, 80)( 51, 66, 83) ( 53, 69, 87)( 54, 70, 89)( 57, 74, 93)( 58, 75, 95)( 60, 77, 98) ( 63, 81,103)( 64, 76, 96)( 67, 84,107)( 71, 90,114)( 72, 91,116) ( 78, 99,124)( 79,100,126)( 82,104,131)( 85,108,112)( 86,109,135) ( 88,111,138)( 92,117,123)( 94,119,125)( 97,122,148)(101,127,150) (102,128,151)(106,132,155)(110,136,160)(113,139,162)(115,141,165) (118,143,168)(120,145,171)(121,146,173)(129,144,169)(130,152,180) (133,156,182)(134,157,184)(140,163,191)(142,166,172)(147,174,198) (149,176,200)(153,181,205)(158,185,207)(159,186,170)(161,188,210) (164,192,214)(167,194,217)(175,199,223)(177,201,224)(178,202,226) (179,203,228)(183,193,215)(187,208,209)(189,211,234)(190,212,221) (195,218,239)(196,219,233)(197,220,242)(204,229,251)(206,231,253) (216,237,255)(222,243,260)(225,246,262)(227,248,257)(230,238,258) (232,254,269)(235,256,267)(240,249,265)(247,263,261)(250,264,268) (252,266,272)(270,271,273) ]), [[1,2]] );