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C₂×#61587 #10577186

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

Aliases

Subgroups

9140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484382);