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C₂×#540199 #72297378

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

Aliases

Subgroups

54165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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