Finite Group Databasebeta

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C₂×#686906 #72260331

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

Aliases

Subgroups

83175 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((1,2), (4,6)(7,8)(9,10)(12,14)(16,19)(20,21), (4,6)(8,9)(15,16,18,19)(17,21,22,20), (11,12)(13,14)(15,17)(16,20)(18,22)(19,21), (3,4,5,6)(7,9,10,8)(11,12)(13,14)(15,17)(16,21)(18,22)(19,20), (15,16)(17,20)(18,19)(21,22));