Finite Group Databasebeta

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C₂×#1082739 #72278175

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

Aliases

Subgroups

72403 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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), (12,14)(15,16,18,20)(17,19,21,22), (11,12)(13,14)(17,21)(19,22), (7,8)(9,10)(15,17)(16,19)(18,21)(20,22), (3,4)(5,6)(7,8)(9,10)(15,16)(17,19)(18,20)(21,22), (1,2));