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#6437985

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

Aliases

No aliases for this group.

Subgroups

4468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345181);