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C₂×#687668 #72299471

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

Aliases

Subgroups

61593 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((4,6)(8,10)(12,14)(16,20)(21,22), (4,6)(11,12)(13,14)(15,16)(17,21)(18,22)(19,20), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,17,19,18)(16,21,20,22), (3,4)(5,6)(15,18,19,17)(16,21,20,22), (3,4)(5,6)(15,16)(17,22)(18,21)(19,20), (1,2));