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#6573704

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

Aliases

No aliases for this group.

Subgroups

4411 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|c^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, 6480900);