Finite Group Databasebeta

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D₃×#473 #80942

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 35 points:

(1,4)(2,9)(3,14)(5,19)(6,21)(7,20)(8,22)(10,18)(11,26)(12,25)(13,27)(15,29)(16,31)(17,30)(23,32)(24,28)(33,34,35);(1,3,6,16,7,17,5,15)(2,8,11,23,12,24,10,13)(4,14,21,31,20,30,19,29)(9,22,26,32,25,28,18,27);(1,2,7,12)(3,13,17,23)(4,18,20,26)(5,11,6,10)(8,16,24,15)(9,21,25,19)(14,28,30,22)(27,31,32,29);(34,35)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 13518);