Finite Group Databasebeta

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C₂×#846737 #72298716

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

Aliases

Subgroups

75583 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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