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#7504670

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

Aliases

No aliases for this group.

Subgroups

1893 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=i,b^2=fg,c^2=f,e^2=i,g^2=i,h^2=i,b^a=bf,c^a=cg,d^a=dfg,g^a=gi,h^a=hi,c^b=ch,d^b=df,f^b=fi,g^b=gi,e^c=ei,g^c=gi,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, 7411866);