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#7623666

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

Aliases

No aliases for this group.

Subgroups

1901 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^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,d^b=df,e^b=ei,f^b=fh,h^b=hi,g^c=gi,f^d=fh,h^d=hi

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530862);