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#7622635

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

Aliases

No aliases for this group.

Subgroups

1891 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=g,c^2=gh,e^2=i,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,d^c=di,f^c=fi

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529831);