Finite Group Databasebeta

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C₃×#498909 #72255378

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

4618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3,4)(6,10)(7,13)(8,15)(11,18)(12,16)(19,20)(21,22,23);(5,6,7,11,9,12,13,20)(8,16,17,19,15,10,14,18);(2,4)(6,11)(7,13)(10,18)(12,20)(14,17)(16,19);(6,12)(7,13)(8,15)(18,19)

Conjugacy classes & character table

168 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)(6,10)(7,13)(8,15)(11,18)(12,16)(19,20)(21,22,23), (5,6,7,11,9,12,13,20)(8,16,17,19,15,10,14,18), (2,4)(6,11)(7,13)(10,18)(12,20)(14,17)(16,19), (6,12)(7,13)(8,15)(18,19));