Finite Group Databasebeta

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C₂×#892355 #72332775

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

Aliases

Subgroups

46841 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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