Finite Group Databasebeta

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C₂×#647778 #72311240

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

Aliases

Subgroups

70373 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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