Finite Group Databasebeta

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C₂×#647658 #72310715

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

Aliases

Subgroups

94137 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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