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#6372721

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

Aliases

No aliases for this group.

Subgroups

4409 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 6279917);