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#6451865

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

Aliases

No aliases for this group.

Subgroups

3777 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 6359061);