Finite Group Databasebeta

?

← Prev (#6469083) Next (#6469085) →

#6469084

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

Aliases

No aliases for this group.

Subgroups

1697 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|c^2=g,e^2=gh,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=dhi,f^b=fi,e^c=ei,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, 6376280);