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C₂×#24256 #6442635

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

Aliases

Subgroups

5164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(4,5)(7,8)(9,10)(11,12)(13,17)(14,16)(15,18);(3,4,6,5)(11,12)(13,17)(14,16)(15,18);(8,10)(12,16)(13,14)(17,18);(3,5,6,4)(11,13,15,14)(12,17,18,16)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349831);