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#6379190

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

Aliases

No aliases for this group.

Subgroups

4485 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286386);