Finite Group Databasebeta

?

← Prev (#6437578) Next (#6437580) →

#6437579

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

Aliases

No aliases for this group.

Subgroups

5923 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)(10,23)(16,33)(17,42)(19,32)(20,31)(22,50)(24,35)(25,38)(26,40)(27,39)(28,36)(29,45)(30,46)(34,51)(37,47)(41,44)(43,57)(48,56)(49,55)(52,59)(53,58)(54,63)(60,61)(62,64);(1,3,8,20)(2,9,14,32)(4,16,24,45)(5,17,27,48)(6,19,7,18)(10,33,36,29)(11,37,39,30)(12,15,13,31)(21,41,35,55)(22,43,53,63)(23,49,28,44)(25,47,26,46)(34,54,59,57)(38,56,40,42)(50,64,58,60)(51,62,52,61);(1,4)(2,10)(3,16)(5,22)(6,23)(7,28)(8,24)(9,29)(11,34)(12,35)(13,21)(14,36)(15,41)(17,43)(18,44)(19,49)(20,45)(25,51)(26,52)(27,53)(30,54)(31,55)(32,33)(37,57)(38,58)(39,59)(40,50)(42,60)(46,61)(47,62)(48,63)(56,64);(1,5)(2,11)(3,17)(4,22)(6,25)(7,26)(8,27)(9,30)(10,34)(12,38)(13,40)(14,39)(15,42)(16,43)(18,46)(19,47)(20,48)(21,50)(23,51)(24,53)(28,52)(29,54)(31,56)(32,37)(33,57)(35,58)(36,59)(41,60)(44,61)(45,63)(49,62)(55,64);(1,6,8,7)(2,12,14,13)(3,18,20,19)(4,23,24,28)(5,25,27,26)(9,31,32,15)(10,35,36,21)(11,38,39,40)(16,44,45,49)(17,46,48,47)(22,51,53,52)(29,55,33,41)(30,56,37,42)(34,58,59,50)(43,61,63,62)(54,64,57,60)

Polycyclic presentation:

2^9|b^2=i,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,e^b=ei,f^b=fi,g^b=gi,g^c=gi,f^d=fi

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344775);