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#7622507

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

Aliases

No aliases for this group.

Subgroups

3933 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=g,e^2=i,f^2=h,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, 7529703);