Finite Group Databasebeta

?

← Prev (#7623025) Next (#7623027) →

#7623026

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

Aliases

No aliases for this group.

Subgroups

1451 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=fh,b^2=f,e^2=i,f^2=i,g^2=h,h^2=i,b^a=bf,c^a=cg,f^a=fi,g^a=gh,h^a=hi,d^b=di,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, 7530222);