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#6379184

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

Aliases

No aliases for this group.

Subgroups

4517 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,e^2=i,f^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, 6286380);