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#6573706

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

Aliases

No aliases for this group.

Subgroups

4396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|c^2=i,d^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, 6480902);