Finite Group Databasebeta

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C₂×C₃×#216 #64066

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

139 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

(3,4,5)(6,7,8)(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17);(4,5)(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18);(1,2)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 714);