Finite Group Databasebeta

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C₂×#855281 #72294086

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

Aliases

Subgroups

61163 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(12,14)(15,16,18,20)(17,21,22,19), (4,6)(11,12,13,14)(15,16,18,20)(17,21,22,19), (8,10)(11,12)(13,14)(15,16,18,20)(17,19,22,21), (4,6)(7,8)(9,10)(15,16)(17,21)(18,20)(19,22), (3,4)(5,6)(15,17)(16,19)(18,22)(20,21), (1,2));