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#6369205

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

Aliases

No aliases for this group.

Subgroups

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,c^2=h,e^2=hi,f^2=h,g^2=i,b^a=bf,c^a=cg,e^a=ehi,f^a=fh,g^a=gi,c^b=ci,d^b=df,e^b=ei,f^b=fh,e^c=eh,g^c=gi,e^d=ei,f^d=fh

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276401);