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#6372742

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

Aliases

No aliases for this group.

Subgroups

4437 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,d^2=h,h^2=i,b^a=bf,c^a=cg,e^a=ei,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, 6279938);