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#27187323

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 117 points:

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

Polycyclic presentation:

2^7,101|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,d^a=dg,h^a=h^91,d^b=dg,f^b=fg,h^b=h^10,h^c=h^100,h^f=h^100

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 20701);