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#6632119

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

Aliases

No aliases for this group.

Subgroups

2134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

53 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6539315);