Finite Group Databasebeta

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C₂²×#37648 #72279029

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

Aliases

Subgroups

145109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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