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#153706

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

Aliases

No aliases for this group.

Subgroups

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|d^2=ef,e^2=fg,f^2=gh,g^2=hi,h^2=i,b^a=bd,c^a=ci,d^a=de,e^a=ef,f^a=fg,g^a=gh,h^a=hi,d^b=de,e^b=ef,f^b=fg,g^b=gh,h^b=hi

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60902);