Finite Group Databasebeta

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D₄×#2177 #72225577

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4641 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(10,15)(11,14)(12,20)(16,23)(17,21)(18,24)(19,22);(9,10)(11,16)(12,21)(13,18)(14,17)(15,20)(19,24)(22,23);(6,7)(10,15)(11,14)(12,20)(16,23)(17,21)(18,24)(19,22);(1,2,3,4)(5,6,8,7)(9,11,13,14)(10,16,18,17)(12,19,22,20)(15,21,24,23);(5,7,8,6)(9,11,13,14)(10,17,18,16)(12,19,22,20)(15,23,24,21)

Conjugacy classes & character table

160 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((10,15)(11,14)(12,20)(16,23)(17,21)(18,24)(19,22), (9,10)(11,16)(12,21)(13,18)(14,17)(15,20)(19,24)(22,23), (6,7)(10,15)(11,14)(12,20)(16,23)(17,21)(18,24)(19,22), (1,2,3,4)(5,6,8,7)(9,11,13,14)(10,16,18,17)(12,19,22,20)(15,21,24,23), (5,7,8,6)(9,11,13,14)(10,17,18,16)(12,19,22,20)(15,23,24,21));