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C₂×#14140 #514578

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

Aliases

Subgroups

7998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421774);