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#27139952

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 161 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)(99,105)(100,111)(101,112)(102,117)(103,121)(106,107)(108,136)(109,138)(110,127)(113,144)(114,147)(115,128)(116,124)(118,152)(119,132)(120,125)(122,135)(123,126)(129,149)(130,148)(131,134)(133,154)(137,161)(139,140)(141,145)(142,143)(146,160)(150,157)(151,156)(153,159)(155,158);(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)(98,99,104,110)(100,105,115,127)(101,116,119,150)(102,120,122,153)(103,123,121,109)(106,128,131,111)(107,132,134,112)(108,135,137,117)(113,136,146,161)(114,138,145,126)(118,151,142,149)(124,155,157,140)(125,158,159,139)(129,160,156,144)(130,141,154,147)(133,143,148,152)

Polycyclic presentation:

2^7,97|a^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^96,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^96

Conjugacy classes & character table

3107 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 2726);