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C₂×#524535 #72313099

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

Aliases

Subgroups

78729 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((8,10)(12,14)(15,16)(17,18)(19,20)(21,22), (4,6)(16,20)(18,21), (1,2), (7,8)(9,10)(11,12,13,14)(16,20)(17,22), (15,17)(16,21)(18,20)(19,22), (3,4,5,6)(15,18,19,21)(16,17,20,22));