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C₈×#443 #184009

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

Aliases

Subgroups

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,5,4,6,7,8);(9,10,13,17,14,11,18,16)(12,15,20,23,21,19,24,22);(9,11)(10,14)(12,19)(13,16)(15,21)(17,18)(20,22)(23,24);(9,12,13,20,14,21,18,24)(10,15,17,23,11,19,16,22)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 91205);