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#6437588

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

Aliases

No aliases for this group.

Subgroups

5915 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344784);