← Prev (#34067327) Next (#34067329) →
Dic4832 #34067328
Aliases
Splittings
Subgroups
36 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 279 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)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279);(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)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,273)(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)(144,265)(145,264)(146,263)(147,262)(148,261)(149,260)(150,259)(151,258)(152,257)(153,256)(154,255)(155,254)(156,253)(157,252)(158,251)(159,250)(160,249)(161,248)(162,247)(163,246)(164,245)(165,244)(166,243)(167,242)(168,241)(169,240)(170,239)(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)
Polycyclic presentation:
2^7,151|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^150,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^150
Conjugacy classes & character table
4835 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 2728);
Finite Group Databasebeta