Finite Group Databasebeta

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C₂×#515363 #72333244

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

Aliases

Subgroups

103669 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(11,12,13,14)(16,19)(17,21), (15,16)(17,20)(18,19)(21,22), (1,2), (8,10)(17,21)(20,22), (3,4)(5,6)(7,8,9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22), (15,17,18,21)(16,20,19,22));