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#34185752

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

380 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)(81,87)(82,91)(84,90)(85,86)(88,93)(89,92)(94,95)(96,99,101,111)(97,103,104,118)(98,106,107,121)(100,113,114,110)(102,115,117,126)(105,119,112,109)(108,125,123,122)(116,127,124,120);(80,82,84,87,85,93,95,92)(81,86,88,94,89,83,91,90)(96,98)(97,102,104,117)(99,106)(100,108)(101,107)(103,115,118,126)(105,116,112,124)(109,120,119,127)(110,122)(111,121)(113,125)(114,123);(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)(82,90,93,94)(83,87,86,92)(84,88)(85,89)(91,95)(96,97)(98,102,107,117)(99,109)(100,112)(101,104)(103,110)(105,114)(106,120,121,127)(108,124,123,116)(111,119)(113,118)(115,125,126,122)

Polycyclic presentation:

2^8,79|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eg,f^c=fgh,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, 67051);