Finite Group Databasebeta

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#27173200

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

154 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 133 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)(102,105)(103,110)(104,114)(106,118)(107,124)(108,120)(109,125)(111,126)(112,129)(113,128)(115,131)(116,132)(117,123)(119,122)(121,127)(130,133);(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)(102,104,106,115,108,116,122,107)(103,109,111,112,113,123,121,130)(105,114,118,131,120,132,119,124)(110,125,126,129,128,117,127,133);(102,103)(104,112)(105,117)(106,121)(107,123)(108,113)(109,115)(110,114)(111,122)(116,130)(118,129)(119,133)(120,125)(124,126)(127,131)(128,132)

Polycyclic presentation:

2^7,101|b^2=d,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^100,e^c=ef,f^c=fg,h^c=h^100

Conjugacy classes & character table

823 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 6578);