Finite Group Databasebeta

?

← Prev (#6573732) Next (#6573734) →

#6573733

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

Aliases

No aliases for this group.

Subgroups

4445 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6480929);