Finite Group Databasebeta

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#34185221

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 127 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)(80,83)(81,86)(82,88)(84,91)(85,92)(87,90)(89,94)(93,95)(96,99)(97,104)(98,108)(100,113)(101,112)(102,114)(103,117)(105,121)(106,120)(107,122)(109,126)(110,125)(111,115)(116,124)(118,127)(119,123);(80,82)(81,85,87,93)(83,88)(84,89)(86,92,90,95)(91,94)(96,98,100,109,102,110,101,116)(97,103,105,107,106,119,115,118)(99,108,113,126,114,125,112,124)(104,117,121,122,120,123,111,127);(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)(82,85,89,93)(83,90,91,86)(84,87)(88,92)(94,95)(96,97)(98,107)(99,111,114,121)(100,115)(101,105)(102,106)(103,109)(104,113,120,112)(108,123,125,117)(110,118)(116,119)(122,124,127,126)

Polycyclic presentation:

2^8,79|a^2=f,b^2=df,d^2=gh,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=egh,f^c=fg,i^c=i^78

Conjugacy classes & character table

1282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 66520);