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#6437953

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

Aliases

No aliases for this group.

Subgroups

4469 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345149);