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Dic4768 #34042909
Aliases
Splittings
Subgroups
36 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 277 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277);(1,65,33,97)(2,66,34,98)(3,67,35,99)(4,68,36,100)(5,69,37,101)(6,70,38,102)(7,71,39,103)(8,72,40,104)(9,73,41,105)(10,74,42,106)(11,75,43,107)(12,76,44,108)(13,77,45,109)(14,78,46,110)(15,79,47,111)(16,80,48,112)(17,81,49,113)(18,82,50,114)(19,83,51,115)(20,84,52,116)(21,85,53,117)(22,86,54,118)(23,87,55,119)(24,88,56,120)(25,89,57,121)(26,90,58,122)(27,91,59,123)(28,92,60,124)(29,93,61,125)(30,94,62,126)(31,95,63,127)(32,96,64,128)(130,277)(131,276)(132,275)(133,274)(134,273)(135,272)(136,271)(137,270)(138,269)(139,268)(140,267)(141,266)(142,265)(143,264)(144,263)(145,262)(146,261)(147,260)(148,259)(149,258)(150,257)(151,256)(152,255)(153,254)(154,253)(155,252)(156,251)(157,250)(158,249)(159,248)(160,247)(161,246)(162,245)(163,244)(164,243)(165,242)(166,241)(167,240)(168,239)(169,238)(170,237)(171,236)(172,235)(173,234)(174,233)(175,232)(176,231)(177,230)(178,229)(179,228)(180,227)(181,226)(182,225)(183,224)(184,223)(185,222)(186,221)(187,220)(188,219)(189,218)(190,217)(191,216)(192,215)(193,214)(194,213)(195,212)(196,211)(197,210)(198,209)(199,208)(200,207)(201,206)(202,205)(203,204)
Polycyclic presentation:
2^7,149|a^2=g,b^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^148,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^148
Conjugacy classes & character table
4771 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 2728);
Finite Group Databasebeta