Finite Group Databasebeta

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C₂×#5955329 #72331112

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

Aliases

Subgroups

72157 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(8,10)(12,14)(15,16,18,21)(17,20,22,19);(4,6)(8,10)(11,12)(13,14)(15,17,18,22)(16,19,21,20);(15,17)(16,20)(18,22)(19,21);(1,2);(3,4,5,6)(7,8)(9,10)(15,17)(16,20)(18,22)(19,21);(15,16)(17,20)(18,21)(19,22)

Conjugacy classes & character table

208 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((8,10)(12,14)(15,16,18,21)(17,20,22,19), (4,6)(8,10)(11,12)(13,14)(15,17,18,22)(16,19,21,20), (15,17)(16,20)(18,22)(19,21), (1,2), (3,4,5,6)(7,8)(9,10)(15,17)(16,20)(18,22)(19,21), (15,16)(17,20)(18,21)(19,22));