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C₂×#14519 #520973

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

Aliases

Subgroups

8478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 428169);