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#7623661

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

Aliases

No aliases for this group.

Subgroups

1897 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530857);