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D₄×#2308 #72334294

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

Aliases

Subgroups

76341 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

220 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((1,2)(3,4)(5,6,8,7)(10,12)(15,19)(18,20), (2,4)(6,7)(9,10)(11,12)(14,17)(18,20), (10,12), (9,10)(11,12), (1,2)(3,4)(5,7,8,6)(13,14)(15,20)(16,17)(18,19), (13,15)(14,18)(16,19)(17,20));