Finite Group Databasebeta

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D₃×#13334 #72271620

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

3248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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