Finite Group Databasebeta

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D₃×#12874 #72269899

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

2028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

120 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)(6,16,18,30)(7,20)(8,22)(10,23,15,24)(11,27)(12,13)(17,31,32,29)(19,28)(21,33)(25,35,26,34), (4,6,7,16,8,17,20,29,9,18,21,30,22,32,33,31)(5,10,11,24,13,26,27,34,14,15,19,23,12,25,28,35), (4,5)(6,15)(7,19)(8,13)(9,14)(10,18)(11,21)(12,22)(16,24)(17,25)(20,28)(23,30)(26,32)(27,33)(29,34)(31,35));