Finite Group Databasebeta

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C₂×#616961 #72256556

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

Aliases

Subgroups

182397 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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