Finite Group Databasebeta

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D₃×#737 #92381

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

219 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 30 points:

(2,3)(4,13,28,7,22,12,14,6,21)(5,20,26,11,18,19,9,10,27)(8,23,30,15,25,24,17,16,29);(1,2,3)(5,9,11)(8,15,17)(10,18,20)(16,23,25)(19,26,27)(24,29,30);(4,5,8)(6,10,16)(7,11,15)(9,17,14)(12,19,24)(13,20,23)(18,25,22)(21,27,29)(26,30,28)

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 226);