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D6016 #26104191
Aliases
Splittings
Subgroups
46 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 175 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)(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);(2,128)(3,127)(4,126)(5,125)(6,124)(7,123)(8,122)(9,121)(10,120)(11,119)(12,118)(13,117)(14,116)(15,115)(16,114)(17,113)(18,112)(19,111)(20,110)(21,109)(22,108)(23,107)(24,106)(25,105)(26,104)(27,103)(28,102)(29,101)(30,100)(31,99)(32,98)(33,97)(34,96)(35,95)(36,94)(37,93)(38,92)(39,91)(40,90)(41,89)(42,88)(43,87)(44,86)(45,85)(46,84)(47,83)(48,82)(49,81)(50,80)(51,79)(52,78)(53,77)(54,76)(55,75)(56,74)(57,73)(58,72)(59,71)(60,70)(61,69)(62,68)(63,67)(64,66)(130,175)(131,174)(132,173)(133,172)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)(141,164)(142,163)(143,162)(144,161)(145,160)(146,159)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)
Polycyclic presentation:
2^8,47|c^2=de,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,g^a=gh,i^a=i^46,c^b=cd,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^b=i^46
Conjugacy classes & character table
3011 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 57481);
Finite Group Databasebeta