Finite Group Databasebeta

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C₃×#128073 #72249303

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2,3)(4,5)(6,10,11,8)(7,9)(13,16)(17,18);(4,6)(5,8)(7,11)(9,10)(12,13,14,18,15,17,19,16);(5,9)(8,10)(13,17)(16,18)

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(4,5)(6,10,11,8)(7,9)(13,16)(17,18), (4,6)(5,8)(7,11)(9,10)(12,13,14,18,15,17,19,16), (5,9)(8,10)(13,17)(16,18));