Finite Group Databasebeta

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C₂²×#59808 #72293714

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

Aliases

Subgroups

146149 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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