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#7514145

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

Aliases

No aliases for this group.

Subgroups

3029 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7421341);