Finite Group Databasebeta

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#34180810

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

656 conjugacy classes of subgroups; only the 107 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)(80,83,85,84)(81,87,88,89)(82,91,92,93)(86,94,90,95)(96,99,101,112)(97,103,105,110)(98,107,109,123)(100,111,114,127)(102,115,116,124)(104,117,119,125)(106,120,118,121)(108,122,113,126);(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)(80,82,85,92)(81,86,88,90)(83,91,84,93)(87,94,89,95)(96,98)(97,102)(99,107)(100,113)(101,109)(103,115)(104,118)(105,116)(106,119)(108,114)(110,124)(111,126)(112,123)(117,121)(120,125)(122,127);(80,81,84,89,85,88,83,87)(82,90,91,95,92,86,93,94)(96,97)(98,106,109,118)(99,110,112,103)(100,104)(101,105)(102,108,116,113)(107,121)(111,125,127,117)(114,119)(115,122)(120,123)(124,126)

Polycyclic presentation:

2^8,79|a^2=f,b^2=g,c^2=gh,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fgh,i^b=i^78,f^c=fh,i^c=i^78

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 62109);