Finite Group Databasebeta

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#27195118

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^7,103|a^2=f,b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^102,f^c=fg,h^c=h^102

Conjugacy classes & character table

1151 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 4484);