Finite Group Databasebeta

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C₂×#609884 #72233053

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

Aliases

Subgroups

83665 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((1,2), (15,16,18,20)(17,19,21,22), (7,8)(9,10)(11,12)(13,14), (3,4)(5,6)(15,17)(16,19)(18,21)(20,22), (4,6)(12,14), (8,10)(17,21)(19,22));