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#6573701

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

Aliases

No aliases for this group.

Subgroups

4383 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6480897);