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#6438012

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

Aliases

No aliases for this group.

Subgroups

4502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345208);