Finite Group Databasebeta

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C₃×#115204 #72248676

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5622 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)(16,19);(8,10)(12,13,15,17)(14,16,18,19);(4,6)(5,8)(7,11)(9,10)(12,14)(13,16)(15,18)(17,19)

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