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#7622849

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

Aliases

No aliases for this group.

Subgroups

3827 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 7530045);