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#6629050

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

Aliases

No aliases for this group.

Subgroups

4401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536246);