Finite Group Databasebeta

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D₉×#1898 #72268784

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

5619 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

(14,16)(15,19)(17,20)(18,21);(5,7)(6,9,10,12)(8,11)(13,20,21,15,14,16,19,18,17);(2,4);(1,2)(3,4)(5,6)(7,9,11,12)(8,10)

Conjugacy classes & character table

192 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((14,16)(15,19)(17,20)(18,21), (5,7)(6,9,10,12)(8,11)(13,20,21,15,14,16,19,18,17), (2,4), (1,2)(3,4)(5,6)(7,9,11,12)(8,10));