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C₂×#35533 #7628912

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

Aliases

Subgroups

12902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536108);