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#7622636

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

Aliases

No aliases for this group.

Subgroups

1871 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529832);