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#6437577

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

Aliases

No aliases for this group.

Subgroups

5917 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|c^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,g^b=gi,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, 6344773);