Finite Group Databasebeta

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C₂×#648053 #72337821

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

Aliases

Subgroups

138259 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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