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#7623143

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

Aliases

No aliases for this group.

Subgroups

1476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530339);