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#6573707

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

Aliases

No aliases for this group.

Subgroups

4426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|e^2=i,f^2=i,h^2=i,b^a=bf,c^a=cg,d^a=di,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

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6480903);