Finite Group Databasebeta

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C₂²×#39339 #72293715

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

Aliases

Subgroups

145637 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((5,6)(7,8)(10,12)(13,14,16,17)(15,19,20,18), (5,6)(7,8)(9,10,11,12)(14,17)(18,19), (13,14)(15,18)(16,17)(19,20), (5,6,7,8), (5,6)(7,8)(13,15,16,20)(14,18,17,19), (3,4), (1,2)(3,4));