Finite Group Databasebeta

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#27206916

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

No aliases for this group.

Splittings

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 135 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)(104,107)(105,113)(106,119)(108,125)(109,122)(110,123)(111,127)(112,114)(115,129)(116,131)(117,133)(118,124)(120,135)(121,134)(126,128)(130,132);(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)(104,107)(105,112)(106,118)(108,122)(109,125)(110,123)(111,126)(113,114)(115,131)(116,129)(117,133)(119,124)(120,134)(121,135)(127,128)(130,132);(104,106,110,121)(105,111,116,128)(107,118,123,135)(108,124,109,120)(112,126,129,127)(113,130,131,133)(114,132,115,117)(119,125,134,122);(104,105,110,116)(106,117,121,132)(107,113,123,131)(108,115,109,114)(111,124,128,120)(112,125,129,122)(118,126,135,127)(119,133,134,130)

Polycyclic presentation:

2^7,103|a^2=g,b^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,f^c=fg,h^c=h^102,e^d=eg,h^d=h^102

Conjugacy classes & character table

842 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 16282);