Finite Group Databasebeta

?

← Prev (#6443341) Next (#6443343) →

#6443342

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

Aliases

No aliases for this group.

Subgroups

4857 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)(10,25)(16,31)(17,42)(19,34)(20,33)(22,50)(23,49)(24,36)(26,39)(27,55)(28,37)(29,40)(30,38)(32,46)(35,53)(41,45)(43,56)(44,48)(47,57)(51,64)(52,59)(54,58)(60,62)(61,63);(1,3,6,18,8,20,7,19)(2,9,13,15,14,34,12,33)(4,22,25,44,26,16,24,45)(5,27,29,46,30,17,28,47)(10,31,21,48,36,50,39,41)(11,32,37,55,38,57,40,42)(23,43,52,61,54,51,53,62)(35,56,58,60,59,64,49,63);(1,4,7,25,8,26,6,24)(2,10,12,21,14,36,13,39)(3,16,19,45,20,22,18,44)(5,23,29,53,30,54,28,52)(9,31,33,48,34,50,15,41)(11,35,37,49,38,59,40,58)(17,43,47,62,27,51,46,61)(32,56,55,63,57,64,42,60);(1,5)(2,11)(3,17)(4,23)(6,28)(7,29)(8,30)(9,32)(10,35)(12,37)(13,40)(14,38)(15,42)(16,43)(18,46)(19,47)(20,27)(21,49)(22,51)(24,52)(25,53)(26,54)(31,56)(33,55)(34,57)(36,59)(39,58)(41,60)(44,61)(45,62)(48,63)(50,64);(1,6,8,7)(2,12,14,13)(3,18,20,19)(4,24,26,25)(5,28,30,29)(9,33,34,15)(10,21,36,39)(11,37,38,40)(16,44,22,45)(17,46,27,47)(23,52,54,53)(31,48,50,41)(32,55,57,42)(35,49,59,58)(43,61,51,62)(56,63,64,60)

Polycyclic presentation:

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

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, 6350538);