Finite Group Databasebeta

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#34115883

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 169 points:

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

Polycyclic presentation:

2^7,157|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,h^a=h^156,d^b=dg,h^b=h^129,h^c=h^156,h^f=h^156

Conjugacy classes & character table

824 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 20257);