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#153586

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monolithic
• monomial

Aliases

No aliases for this group.

Subgroups

113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 128 points:

(1,2,6,13,7,14,35,56,8,15,36,57,38,60,90,111,5,16,31,58,32,61,86,112,33,63,42,93,87,114,95,124,9,17,37,59,39,62,91,113,40,19,64,68,92,69,115,118,34,12,52,53,88,54,107,108,89,55,96,109,123,110,125,128)(3,18,21,65,22,66,72,116,23,67,46,100,74,117,101,127,24,45,73,98,75,99,119,126,77,4,11,27,47,28,48,81,25,29,49,82,76,84,104,121,78,26,50,79,102,80,105,120,20,10,41,43,70,44,94,97,71,30,51,83,103,85,106,122);(1,3)(2,10)(4,19)(5,24)(6,21)(7,22)(8,23)(9,25)(11,42)(12,29)(13,43)(14,44)(15,30)(16,18)(17,45)(20,34)(26,55)(27,68)(28,69)(31,73)(32,75)(33,77)(35,72)(36,46)(37,49)(38,74)(39,76)(40,78)(41,52)(47,87)(48,95)(50,64)(51,96)(53,82)(54,84)(56,97)(57,83)(58,65)(59,98)(60,85)(61,66)(62,99)(63,67)(70,88)(71,89)(79,109)(80,110)(81,118)(86,119)(90,101)(91,104)(92,102)(93,100)(94,107)(103,123)(105,115)(106,125)(108,121)(111,122)(112,116)(113,126)(114,117)(120,128)(124,127);(1,4,6,27,7,28,35,81,8,29,36,82,38,84,90,121,5,26,31,79,32,80,86,120,33,10,42,43,87,44,95,97,9,30,37,83,39,85,91,122,40,18,64,65,92,66,115,116,34,67,52,100,88,117,107,127,89,45,96,98,123,99,125,126)(2,11,13,47,14,48,56,25,15,49,57,76,60,104,111,78,16,50,58,102,61,105,112,20,63,41,93,70,114,94,124,71,17,51,59,103,62,106,113,3,19,21,68,22,69,72,118,23,12,46,53,74,54,101,108,24,55,73,109,75,110,119,128,77)

Polycyclic presentation:

2^9|a^2=e,c^2=e,d^2=i,e^2=f,f^2=g,g^2=h,h^2=i,b^a=bd,d^a=di,d^b=di

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60782);