Finite Group Databasebeta

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C₂×#156815 #72294875

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

Aliases

Subgroups

135205 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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