Finite Group Databasebeta

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C₂×#1418447 #72297408

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

Aliases

Subgroups

54431 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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