Finite Group Databasebeta

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C₂×#650484 #72325535

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

Aliases

Subgroups

61017 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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