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#6368673

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

Aliases

No aliases for this group.

Subgroups

1483 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

59 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6275869);