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#6438016

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

Aliases

No aliases for this group.

Subgroups

4485 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 6345212);