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C₂×#542 #3454

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

Aliases

Subgroups

566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2186);