Finite Group Databasebeta

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#27208276

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 135 points:

(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)(104,107,110,109)(105,113,112,124)(106,116,118,125)(108,119,123,122)(111,127,126,128)(114,120,129,134)(115,132,131,130)(117,121,133,135);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(105,112)(111,126)(113,124)(114,129)(115,131)(120,134)(127,128)(130,132);(104,106)(105,111)(107,116)(108,121)(109,125)(110,118)(112,126)(113,127)(114,130)(115,120)(117,122)(119,133)(123,135)(124,128)(129,132)(131,134);(104,105)(106,115)(107,113)(108,120)(109,124)(110,112)(111,117)(114,122)(116,132)(118,131)(119,129)(121,127)(123,134)(125,130)(126,133)(128,135)

Polycyclic presentation:

2^7,103|d^2=g,e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,e^b=ef,f^b=fg,h^d=h^102

Conjugacy classes & character table

848 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 17642);