Finite Group Databasebeta

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C₂×#647682 #72286804

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

Aliases

Subgroups

164769 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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