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C₂×#1082742 #72294453

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

Aliases

Subgroups

65243 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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)(15,16,18,20)(17,21,22,19), (11,12)(13,14)(15,16,18,20)(17,19,22,21), (4,6)(8,10)(15,16,18,20)(17,21,22,19), (7,8)(9,10)(15,16)(17,19)(18,20)(21,22), (3,4)(5,6)(7,8)(9,10)(15,17)(16,19)(18,22)(20,21), (1,2));