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C₈×#508 #483495

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

Aliases

Subgroups

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 40 points:

(1,2,3,5,4,6,7,8);(9,10)(11,20)(12,17)(13,25)(14,29)(15,19)(16,22)(18,27)(21,36)(23,37)(24,35)(26,31)(28,39)(30,34)(32,40)(33,38);(9,11)(10,16)(12,21)(13,26)(14,30)(15,23)(17,31)(18,34)(19,33)(20,25)(22,27)(24,38)(28,40)(29,32)(35,36)(37,39);(9,12,15,14)(10,17,19,29)(11,21,23,30)(13,24,28,27)(16,31,33,32)(18,25,35,39)(20,36,37,34)(22,26,38,40)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390691);