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#6379195

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

Aliases

No aliases for this group.

Subgroups

4503 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,f^2=i,g^2=i,b^a=bf,c^a=cg,e^a=ei,f^a=fi,d^b=df,f^b=fi,g^c=gi,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, 6286391);