Finite Group Databasebeta

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C₂×#532351 #72299418

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

Aliases

Subgroups

54985 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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