Finite Group Databasebeta

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C₂²×#59095 #72291747

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

Aliases

Subgroups

150329 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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