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C₂×#2077215 #72296421

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

Aliases

Subgroups

50119 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(12,14)(15,16)(17,20)(18,22)(19,21), (11,12)(13,14)(15,17)(16,20)(18,21)(19,22), (8,10)(16,21)(17,22), (4,6)(8,10)(15,18,19,20)(16,22,21,17), (3,4)(5,6)(7,8)(9,10)(15,16)(17,18)(19,21)(20,22), (1,2));