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C₂×#648451 #72331149

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

Aliases

Subgroups

66871 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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), (7,8)(9,10)(11,12)(13,14)(15,16,19,22)(17,21,18,20), (7,8)(9,10)(15,17,19,18)(16,20,22,21), (1,2), (4,6)(7,8,9,10)(15,16)(17,21)(18,20)(19,22), (3,4)(5,6)(7,8)(9,10)(15,18,19,17)(16,21,22,20));