Finite Group Databasebeta

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D₃×#13200 #72270403

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

156 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)(10,22)(14,26)(23,32)(27,28), (4,6,7,15,8,17,19,30,9,16,20,29,21,31,34,35)(5,10,11,23,13,14,24,27,12,22,18,32,25,26,33,28), (4,5)(6,14,16,26)(7,18)(8,13)(9,12)(10,17,22,31)(11,20)(15,28,29,27)(19,33)(21,25)(23,35,32,30)(24,34));