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#153583

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

Aliases

No aliases for this group.

Subgroups

103 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60779);