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#7623149

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

Aliases

No aliases for this group.

Subgroups

1456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

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, 7530345);