Finite Group Databasebeta

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D₃×#13310 #72271656

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

3168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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