Finite Group Databasebeta

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C₂²×#44877 #72236664

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

Aliases

Subgroups

162281 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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