Finite Group Databasebeta

?

← Prev (#6451785) Next (#6451787) →

#6451786

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

Aliases

No aliases for this group.

Subgroups

3745 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,c^2=g,d^2=g,e^2=i,f^2=i,h^2=i,b^a=bf,c^a=cg,f^a=fi,h^a=hi,c^b=ch,d^b=dh,f^b=fi,g^b=gi,h^b=hi,e^c=ei,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, 6358982);