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#34185249

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

400 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)(81,87)(83,84)(86,94)(88,89)(90,95)(91,93)(96,99)(97,103)(98,107)(100,114)(101,111)(102,115)(104,110)(105,121)(106,112)(108,122)(109,124)(113,123)(116,127)(117,125)(118,119)(120,126);(80,82)(81,86,89,95)(83,91)(84,93)(85,92)(87,94,88,90)(96,98,106,109,101,108,100,113)(97,102,105,120,104,117,119,116)(99,107,112,124,111,122,114,123)(103,115,121,126,110,125,118,127);(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)(80,81,83,87,85,89,84,88)(82,90,91,86,92,94,93,95)(96,97,100,105,101,104,106,119)(98,102,109,116,108,117,113,120)(99,110,112,121,111,103,114,118)(107,115,123,126,122,125,124,127)

Polycyclic presentation:

2^8,79|a^2=f,b^2=dfg,d^2=gh,e^2=gh,f^2=g,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, 66548);