Finite Group Databasebeta

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#27172838

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 137 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)(106,109,112,111)(107,114,116,126)(108,118,120,127)(110,121,125,124)(113,128,130,129)(115,122,132,136)(117,133,134,131)(119,123,135,137);(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)(106,108)(107,113)(109,118)(110,123)(111,127)(112,120)(114,128)(115,131)(116,130)(117,122)(119,124)(121,135)(125,137)(126,129)(132,133)(134,136);(102,103,104,105)(106,107)(108,117)(109,114)(110,122)(111,126)(112,116)(113,119)(115,124)(118,133)(120,134)(121,132)(123,128)(125,136)(127,131)(129,137)(130,135)

Polycyclic presentation:

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

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 6216);