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#7623062

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

Aliases

No aliases for this group.

Subgroups

1561 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|c^2=fh,e^2=i,g^2=hi,h^2=i,b^a=bf,c^a=cg,g^a=gh,h^a=hi,d^b=di,g^b=gi,f^c=fi,g^c=ghi,h^c=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, 7530258);