Finite Group Databasebeta

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D₃×#12754 #72248275

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

4984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

102 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((34,35), (1,4,6,16)(2,8,9,21)(3,12,14,27)(5,15,17,30)(7,18,19,20)(10,22,23,32)(11,24,25,31)(13,28,29,26)(33,34,35), (1,3)(2,7,9,19)(4,12)(5,13)(6,14)(8,20,21,18)(10,11,23,25)(15,26)(16,27)(17,29)(22,24,32,31)(28,30), (1,2)(3,11,14,25)(4,8)(5,10)(6,9)(7,13,19,29)(12,24,27,31)(15,22)(16,21)(17,23)(18,28,20,26)(30,32));