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#6628886

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

Aliases

No aliases for this group.

Subgroups

16731 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 64 points:

(1,2,8,14)(3,15,20,31)(4,21,24,38)(5,11,27,37)(6,13,7,12)(9,18,32,19)(10,28,34,23)(16,29,44,55)(17,45,48,40)(22,50,53,57)(25,36,26,35)(30,47,56,46)(33,52,58,51)(39,43,49,42)(41,60,62,54)(59,61,64,63);(1,3)(2,9)(4,16)(5,17)(6,18)(7,19)(8,20)(10,29)(11,30)(12,31)(13,15)(14,32)(21,49)(22,41)(23,42)(24,44)(25,46)(26,47)(27,48)(28,43)(33,54)(34,55)(35,45)(36,40)(37,56)(38,39)(50,64)(51,61)(52,63)(53,62)(57,59)(58,60);(1,4)(2,10)(3,16)(5,22)(6,23)(7,28)(8,24)(9,29)(11,33)(12,21)(13,38)(14,34)(15,39)(17,41)(18,42)(19,43)(20,44)(25,51)(26,52)(27,53)(30,54)(31,49)(32,55)(35,50)(36,57)(37,58)(40,59)(45,64)(46,61)(47,63)(48,62)(56,60);(1,5)(2,11)(3,17)(4,22)(6,25)(7,26)(8,27)(9,30)(10,33)(12,35)(13,36)(14,37)(15,40)(16,41)(18,46)(19,47)(20,48)(21,50)(23,51)(24,53)(28,52)(29,54)(31,45)(32,56)(34,58)(38,57)(39,59)(42,61)(43,63)(44,62)(49,64)(55,60);(1,6,8,7)(2,12,14,13)(3,18,20,19)(4,23,24,28)(5,25,27,26)(9,31,32,15)(10,21,34,38)(11,35,37,36)(16,42,44,43)(17,46,48,47)(22,51,53,52)(29,49,55,39)(30,45,56,40)(33,50,58,57)(41,61,62,63)(54,64,60,59)

Polycyclic presentation:

2^9|a^2=i,e^2=i,f^2=i,g^2=i,b^a=bf,c^a=cg,d^a=dh,e^a=ei,f^a=fi,g^a=gi,f^b=fi,h^b=hi,g^c=gi,f^d=fi

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536082);