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#7622513

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

Aliases

No aliases for this group.

Subgroups

3913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529709);