Finite Group Databasebeta

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#34115420

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 189 points:

(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,87)(48,49)(51,83)(52,53)(55,79)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,116)(69,70)(72,112)(73,74)(76,108)(77,78)(80,104)(81,82)(84,100)(85,86)(88,96)(89,90)(91,92)(93,142)(94,95)(97,140)(98,99)(101,138)(102,103)(105,136)(106,107)(109,133)(110,111)(113,129)(114,115)(117,125)(118,119)(120,121)(122,139)(123,124)(126,137)(127,128)(130,134)(131,132)(141,149)(143,148)(144,145)(146,147)(150,155)(151,152)(153,154)(156,157)(158,161,162,169)(159,164,165,171)(160,167,168,173)(163,170,166,172)(176,183)(179,182)(184,185)(187,189);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,64)(47,66)(49,69)(50,63)(51,62)(53,73)(54,59)(55,58)(57,77)(61,81)(65,85)(67,89)(68,91)(70,94)(71,88)(72,87)(74,98)(75,84)(76,83)(78,102)(79,80)(82,106)(86,110)(90,114)(92,118)(93,120)(95,123)(96,117)(97,116)(99,127)(100,113)(101,112)(103,131)(104,109)(105,108)(107,135)(111,132)(115,128)(119,124)(121,144)(122,146)(125,143)(126,142)(129,141)(130,140)(133,139)(134,138)(136,137)(145,151)(147,153)(148,152)(149,150)(154,157)(155,156)(158,160)(159,163)(161,167)(162,168)(164,170)(165,166)(169,173)(171,172)(174,176)(175,179)(177,185)(178,183)(180,182)(181,189)(184,186)(187,188);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(158,159)(160,166,168,163)(161,164)(162,165)(167,172,173,170)(169,171)(174,175,177,181,178,180,186,188)(176,182,184,189,183,179,185,187)

Polycyclic presentation:

2^7,157|a^2=e,c^2=fg,e^2=g,b^a=bd,d^a=df,h^a=h^129,c^b=cg,e^b=ef,h^b=h^156,h^c=h^156,h^e=h^156

Conjugacy classes & character table

812 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 19794);