Finite Group Databasebeta

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C₂²×#35514 #72293055

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

Aliases

Subgroups

145829 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

256 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((10,11)(14,17)(15,19), (3,4), (6,8)(9,10,12,11)(15,19)(18,20), (14,17)(18,20), (5,6)(7,8)(9,11,12,10)(13,14,16,17)(15,20,19,18), (1,2)(3,4), (13,15,16,19)(14,18,17,20));