Finite Group Databasebeta

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#34102113

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 221 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)(158,161,165,180)(159,167,171,193)(160,173,176,205)(162,178,185,212)(163,186,164,179)(166,189,191,217)(168,192,196,209)(169,197,170,177)(172,199,200,220)(174,202,188,215)(175,204,187,203)(181,208,195,219)(182,210,213,221)(183,214,184,211)(190,216,198,207)(194,218,206,201);(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)(158,160)(159,166)(161,173)(162,182)(163,175)(164,187)(165,176)(167,189)(168,194)(169,190)(170,198)(171,191)(172,181)(174,184)(177,207)(178,210)(179,203)(180,205)(183,188)(185,213)(186,204)(192,218)(193,217)(195,200)(196,206)(197,216)(199,208)(201,209)(202,211)(212,221)(214,215)(219,220);(158,159,165,171)(160,172,176,200)(161,177,180,197)(162,181,185,195)(163,170,164,169)(166,188,191,174)(167,186,193,179)(168,183,196,184)(173,201,205,218)(175,206,187,194)(178,209,212,192)(182,198,213,190)(189,210,217,221)(199,204,220,203)(202,207,215,216)(208,214,219,211)

Polycyclic presentation:

2^7,157|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,h^b=h^156,e^c=eg,h^c=h^156

Conjugacy classes & character table

1739 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 6487);