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C₂×#7653790 #72256238

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

Aliases

Subgroups

118617 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

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